Control 1/90Author(s): LITTOVER, M., LOTMAN, M., RANDVEE, I., TAVAST, R.-R. Title: CIM strategy for Estonian industry. 18 p. (in Estonian) Language: Estonian

Control 2/90Author(s): TENNO, R., OIT, H., LAMP, I., PRAUST, V. Title: Optimal control of stochastic processes. 4 p. (in Estonian). Language: Estonian

Control 3/90Author(s): OIT, M., LAKSPERE, E., NURGES, Y., SOONE, S., ROSS, T. Title: Design of the knowledge base for the technical control object. 7 p. (in Estonian) Language: Estonian ABSTRACT. A new method for the description of the technical control object as an observation base is proposed and possibilities for design of predictive control system based on such object description method are studied. The software for the practical use of that method and for predictive control modelling is implemented. Description of the technical control object in PROLOG language and in the conceptual programming environment CPE is studied and using named means the greenhouse control system is modelled.

Control 4/90Author(s): KOTTA, Ylle. Title: Nonlinear discrete-time dynamic control systems. 6 p. (in Estonian). Language: Estonian ABSTRACT. In the case of the nonlinear discrete-time control system the sufficient conditions are given for the existence of such compensator (control law) that guarantees either (i) the coincidence of the input-output maps of the compensated system and a prespecified model or (ii) invariance of the outputs of the compensated system from input disturbances. Provided these conditions are satisfied the equations of the compensator are obtained in the state- feedback form.

Control 5/90Author(s): KÜNNAP, E., MEISTER, E., OTT, A., RAUDSEPP, M., ROHTLA, M. et al. Title: The study of expert systems of speech synthesis and realization of rule languages. The phonetic studies of the Estonian, Finnish and Russian languages and the modelling of phonologic system in speech synthesis. (in Estonian). Language: Estonian ABSTRACT. The given report summarizes the results of research carried out in the department of speech technology in 1990. For the first time the models of prosodic structure of the Estonian and Finnish languages, used in directing the speech synthesis, are presented. To describe the model of the Russian intonation, the algorithm has been created on the basis of the "contour - Interaction" theory. The scientific aspects, connected with the measurement of the pitch, are described. Hard- and software of the pitch extraction for the computer IBM XT/AT has been made on the basis of the given principles. The comparative analyses of the vocal tract models is also presented.

Control 6/91Author(s): KOTTA, Ylle. Title: The local disturbance decoupling problem for nonlinear discrete-time systems. 6 p. Language: English

Control 7/91Author(s): KOTTA, Ylle. Title: The disturbance decoupling by static state feedback for nonlinear discrete-time systems. 6 p. Language: English

Control 8/91Author(s): KOTTA, Ylle. Title: Model matching of nonlinear discrete time systems in the presence of disturbances. 5 p. Language: English

Control 9/91Author(s): KOTTA, Ylle. Title: Dynamic disturbance decoupling for discrete time nonlinear systems: The non-square andnon-invertible case. 14 p. Language: English

Control 10/91Author(s): KOTTA, Ylle. Title: Inversion methods in the nonlinear control systems design. Pt. 1: (d, ...,d) - delay rightinvertible systems. 52 p. Language: English

Control 11/91Author(s): KOTTA, Ylle. Title: Model matching of nonlinear discrete time systems in the presence of unmeasurabledisturbances. 14 p. Language: English

Control 12/91Author(s): KOTTA, Ylle. Title: The model matching problem for nonlinear systems. The effects of time- discretization .(in Russian) 24 p. Language: Rus

Control 13/91Author(s): KOTTA, Ylle. Title: The model matching problem for discrete-time nonlinear systems. (in Russian) 26 p. Language: Rus

Control 14/91Author(s): NURGES, Ylo. Title: Digital PID controller design via Laguerre model. 4 p. Language: English

Control 15/91Author(s): NURGES, Ylo. Title: Digital controller design in Laguerre domain. 7 p. Language: English

Control 16/91Author(s): NURGES, Ylo. Title: Adaptive predictive control via Laguerre model. (in Russian) 18 p. Language: Rus

Control 17/92Author(s): KOTTA, Ylle. Title: Comments on a structural approach to nonlinear matching problem. 11 p. Language: English Keywords: Nonlinear system; model matching; structure algorithm; regularity; dynamicprecompensation. ABSTRACT. It is shown that the sufficient conditions for solvability of the model matching problem (MMP) in terms of structural invariants, presented by Moog, Perdon and Conte (see SIAM J. Control Optim. 29 (1991), pp. 769-785) are also necessary, and the seeming controversy with the example due to Huiberts is resolved.

Control 18/92Author(s): KOTTA, Ylle. Title: On zero dynamics of discrete-time nonlinear system in the presence of disturbances. 26 p. Language: English

ABSTRACT. The paper considers the output zeroing problem for discrete- time nonlinear system with measurable input disturbances. The objective is to identify, if possible, the set of all pairs consisting of an initial state and a control sequence, which produce an identically zero output for the given disturbance sequence. For this purpose the zero dynamics algorithm is generalized for discrete-time nonlinear system measurable input disturbances. Under some mild regularity assumptions, the local solution around an equilibrium point of the system is derived on the basis of zero dynamics algorithm.

Control 19/92Author(s): KOTTA, Ylle. Title: Decoupling of discrete-time nonlinear systems by minimal order dynamic state feedback. 23p. Language: English ABSTRACT. This paper studies the dynamic input-output decoupling problem for discrete-time nonlinear systems. Using the linear-algebraic framework and inversion algorithm for this class of systems the dynamic state feedback compensator of minimal dimension is obtained that solves the decoupling problem.

Control 20/92Author(s): KOTTA, Ylle. Title: Structural approach to discrete-time nonlinear model matching. 15 p. Language: English Keywords: Discrete systems; nonlinear systems; model matching; structure algorithm. ABSTRACT. The paper considers the problem of designing the compensator for a nonlinear discrete-time plant under which input-output behaviour of the compensated system becomes the same as the one of the prespecified nonlinear model. A local solution, i.e., the necessary and sufficient conditions as well the systematic procedure for constructing a precompensator are given around a regular equilibrium point of the so-called extended system, formed from the plant and the model.The solution is obtained via the inversion (structure) algorithm, which produces the sequence of uniquely defined structural parameters - the invertibility indices. The necessary and sufficient conditions are formulated in terms of these parameters: the problem is solvable if and only if the corresponding invertibility indices of the plant and those of the extended system are equal.

Control 21/92Author(s): KOTTA, Ylle. Title: Dynamic disturbance decoupling for discrete-time nonlinear systems: A solution in terms ofsystem invariants. 31 p. Language: English Keywords: Discrete time systems; nonlinear control systems; disturbance decoupling; inversion algorithm; invertibility indices. ABSTRACT. The paper considers the dynamic disturbance decoupling problem for a discrete-time nonlinear system locally around its equilibrium point. The complete solution to the problem, that is the necessary and sufficient conditions as well the procedure for constructing the compensator, is given both for the cases of measurable and unmeasurable input disturbances under certain regularity assumptions of the equilibrium point. Under the mentioned regularity assumptions of the euilibrium point the solvability conditions for the dynamic disturbance decoupling problem via regular or nonregular dynamic state feedback are shown to be the same. Instrumental in the problem solution are the two versions of the inversion algorithm for discrete-time nonlinear system with disturbances which produce two finite sequences of uniquely defined integers, the so called invertibility indices, either with respect to both inputs or with respect to control only. The necessary and sufficient conditions for local solvability of the problem are derived in terms of the invertibility indices. The inversion algorithm provides also a systematic procedure for constructing the compensator that solves the problem.

Control 22/92Author(s): SESTEROV, Vladimir. Title: Graphical model of a technological object. (in Estonian) 79 p. Language: Estonian ABSTRACT. In that graduation paper instrumental object-oriented system of programming C-Priz is used as tools. C-Priz is used for automation solving task of projecting. It run under MS Windows. Originality of C-Priz is working Scheme Editor, what allow organize graphics interface. Technological object is examined as collection of elements of technological process. Graphic model of elements of technological process is realized in language of C-Priz. For final user every element description is

represented as graphic picture, what simplify understanding system work. A parameters can change on graphic picture too. Methodic for describing elements of technological object and composing control system in Scheme Editor is worked out in the graduation paper.Frequently occurring elements of technological object is examined as examples. Electrical stove temperature stabilization system and tank level control system is made, using before described elements. Volume of elements is enough for solving complicated control tasks. If we want, we can make other model of elements using our methodic.

Control 23/92Author(s): NURGES, Ylo. Title: Robust stability of discrete interval systems. 9 p. Language: English Keywords: Robust stability; discrete systems; interval polynomials. ABSTRACT. A linear-fractional mapping with a free parameter is introduced on the complex plane which transforms the unit circle into itself. This mapping doesn' alter the stability properties of a discrete system. The free parameter variation in a fixed region allows to relax sufficient robust stability conditions.

Control 24/92Author(s): NURGES, Ylo. Title: On the digital controller design with a free parameter. 8 p. Language: English

Control 25/92Author(s): NURGES, Ylo. Title: Robust control for a class of linear systems. 9 p. Language: English

Control 26/92Author(s): NURGES, Ylo. Title: Robust control with a free parameter. 14 p. Language: English Keywords: Robust stability; discrete systems; robust control. ABSTRACT. A linear-fractional mapping with a free parameter is introduced on the complex plane which transforms the unit circle into itself. This mapping doesn't alter the stability properties of a discrete system. The free parameter variation in a fixed region allows to relax sufficient robust stability conditions. Following the modal control algorithm and making use of the linear-fractional mapping with a free parameter it is shown that the stability of the closed loop system is guaranteed for an interval plant if the admissible region of the free parameter is sufficiently large.

Control 27/92Author(s): NURGES, Ylo. Title: Controller design via Laguerre model. (in Russian) 13 p. Language: Rus

Control 28/92Author(s): LITTOVER, Mati, RANDVEE, Ingmar, TAVAST, Raul, VAIN, Jyri. Title: A modelling framework for integrated factory automation. 7 p. Language: English Keywords: Open systems; requirements specification; integration; open-EDI model. ABSTRACT. A possible modelling the knowledge acquisition at the initiation phase of the CIM project life cycle is investigated. CIM system requirements specification framework based on the concepts of autonomous entities, the open- EDI model and requirements specification language KAOS is proposed. An illustrative sample problem is also given.

Control 29/92Author(s): LITTOVER, Mati, RANDVEE, Ingmar, TAVAST, Raul. Title: CIM system architecture for dairies. 6 p. Language: English Keywords: CIM system; reference architecture; enterprise modelling.

ABSTRACT. The structural trend in the food processing industries in recent years has been towards fewer, larger and more specialized production facilities. The efforts to develop a unified CIM approach for dairies based on the CIM project for Estonian industrial enterprises are discussed in the present paper. The architecture for a dairy CIM reference model (DRM) and the associated system of generic active GAE, are described in detail.Also the experiences with implementation of the CIM system in dairy of Paide, Estonia are briefly reported.

Control 30/92Author(s): LITTOVER, Mati, RANDVEE, Ingmar, VAIN, Jyri. Title: Data base design for "AS Tallinna Paber"'s information system. (in Estonian). 19 p. Language: Estonian

Control 31/92Author(s): KURKI-SUONIO, Reino, SYSTA, Kari, VAIN, Jyri. Title: Scheduling in real-time models. 13 p. Language: English Keywords: Executable specifications; fairness; formal methods; interleaving model; joint actions; reactive systems. ABSTRACT. Interleaving semantics is shown to provide an appropriate basis also for the modeling of real-time properties. Real-time scheduling of interleaved actions is explored, and the crucial properties of such schedulings are analyzed. The motivation of the work is twofold: to make real-time modeling practical already at early stages of specification and design, and to increase the reliability and predictability of reactive real-time systems by improved insensitivity to changes in the underlying real-time assumptions.

Control 32/92Author(s): KURKI-SUONIO, Reino, SYSTA, Kari, VAIN, Jyri. Title: Real-time specification and modelling with joint actions. 24 p. Language: English ABSTRACT. The notion of joint actions provides a natural execution model for a specification language,when temporal logic of actions is used for formal reasoning. We extend this basis with scheduling, the role of which is to enforce liveness properties and to introduce real-time properties. This is done in a way that agrees with the partial-order view of computations and can be applied already in early stages of specification and design. This leads to distinguishing between schedulings that are totally correct, partially correct, or incorrect with respect to liveness properties. A general scheduling policy of durational actions is formulated from which any reasonable scheduling can be obtained by reducing its nondeterminism. When this policy is totally correct for a system and gives the required real-time properties, no special limitations are imposed on the implementation. The approach also leads to a general classification of real-time models according to the permitted interactions between the computational state and real time.

Control 33/92Author(s): VAIN, Jyri. Title: Time-invariant transformations of joint action systems. 5 p. Language: English

Control 34/92Author(s): VAIN, Jyri (Ed.) Title: International summer school on real-time fault-tolerance and artificial intelligence, Neeruti (Estonia), June 30 - July 2, 1992. 83 p. Language: English

Control 35/92Author(s): VAIN, Jyri. Title: Developing constructive requirements specifications for CIM systems. 7 p. Language: English Keywords: Industrial technologies; information and communication technologies.

Control 36/92Author(s): TAMM, Boris.

Title: Elements of expert system technology. 46 p. Language: English ABSTRACT. This study is a continuation of the investigation presented in 1991 under the Report No. 5200 and is dedicated to the development of expert systems technology. The work done in 1992 is related to the metrics of heuristical rules, decomposition of knowledge-base structures and design of multidimensional time-depended matrixes whose attributes have to be kept in certain boundary conditions.

Control 36/92Author(s): TAMM, Boris. Title: Elements of expert system technology. 46 p. Language: English ABSTRACT. This study is a continuation of the investigation presented in 1991 under the Report No. 5200 and is dedicated to the development of expert systems technology. The work done in 1992 is related to the metrics of heuristical rules, decomposition of knowledge-base structures and design of multidimensional time-depended matrixes whose attributes have to be kept in certain boundary conditions.

Control 36/92Author(s): TAMM, Boris. Title: Elements of expert system technology. 46 p. Language: English ABSTRACT. This study is a continuation of the investigation presented in 1991 under the Report No. 5200 and is dedicated to the development of expert systems technology. The work done in 1992 is related to the metrics of heuristical rules, decomposition of knowledge-base structures and design of multidimensional time-depended matrixes whose attributes have to be kept in certain boundary conditions.

Control 36/92Author(s): TAMM, Boris. Title: Elements of expert system technology. 46 p. Language: English

Control 37/93Author(s): KOTTA, U., NIJMEIJER, H. Title: On dynamic input-output linearization of discrete-time nonlinear systems. 43 p. Language: English ABSTRACT. This paper studies the problem of linearizing the input-output map of an analytic discrete-time nonlinear system locally around a given trajectory. Necessary and sufficient conditions are given for the existence of a regular dynamic state feedback control law under which the input-dependent part of the response of a nonlinear system becomes linear in the input and independent of the initial state. The proposed conditions are less restrictive than those obtained by Lee and Marcus for linearizing the input-output map via a static state feedback. Instrumental in the problem solution is the inversion (structure) algorithm for discrete-time nonlinear system. Firstly, the solvability conditions are expressed in terms of the inversion algorithm. Secondly, the proof of the existence and construction of the dynamic state feedback compensator relies on this algorithm.

Control 38/93Author(s): KOTTA, U. Title: Essential orders for discrete-time nonlinear system. 13 p. Language: English ABSTRACT. The concept of essential orders has been recently introduced into system theory and has been shown to be useful in the solution of static and dynamic decoupling problems. This paper presents an extension of this notion to the class of discrete-time nonlinear systems, and proves the discrete-time counterparts for some results about essential orders from the theory of continius-time nonlinear systems.

Control 38/93Author(s): KOTTA, U. Title: Essential orders for discrete-time nonlinear system. 13 p.

Language: English ABSTRACT. The concept of essential orders has been recently introduced into system theory and has been shown to be useful in the solution of static and dynamic decoupling problems. This paper presents an extension of this notion to the class of discrete-time nonlinear systems, and proves the discrete-time counterparts for some results about essential orders from the theory of continius-time nonlinear systems.

Control 39/93Author(s): FLIEGNER, Th., NIJMEIJER, H., KOTTA, U. Title: Some aspects of nonlinear discrete-time descriptor systems in economics. 8 p. Language: English ABSTRACT. In this paper we study nonlinear discrete-time descriptor (or singular, implicit, general) systems. One of the first problems connected with such systems, which arise naturally in economic modelling, are questions concerning existence and uniqueness of solutions. By means of a step by step procedure we will give under generic conditions, a local reduction mechanism yielding a lower dimensional system in state space form.

Control 40/93Author(s): NURGES, Ylo. Title: On the robust stability of polytopes. 11 p. Language: English Keywords: Robust stability; discrete-time systems; polytopes. ABSTRACT. A family of stable (Schur) polynomials is generated starting from a single stable polynomial (or polytope) by means of a transform the unit circle into itself. The transform is linear in respect of polynomial coefficients but nonlinear in respect of a free parameter. By repeated use of the transform and the edge theorem a sequence of stable polytopes is produced.

Control 41/93Author(s): NURGES, Ylo. Title: Robust controller for a family of polytopic plants. 14 p. Language: English Keywords: Robust control; stability of polytopes; discrete-time systems. ABSTRACT. By means of the edge theorem and a linear-fractional transform which maps the unit circle into itself some sufficient robust stability conditions are obtained for discrete-time systems. This transform with a free parameter (-1,1) generates a family of plants stabilizable with a single controller. Those robust stability conditions allows us to define a specific family of polytopic plants stabilizable with a single controller.

Control 42/93Author(s): KOTTA, Ylle. Title: Model matching of nonlinear discrete time systems in the presence of disturbances. 36 p. Language: English Keywords: Discrete time systems; nonlinear control systems; model matching; disturbance decoupling; inversion algorithm. ABSTRACT. The paper studies the model matching problem for a discrete time nonlinear system in the presence of input disturbances. Both the cases of measurable and unmeasurable disturbances are considered. Instrumental in the problem solution are two versions of the inversion (structure)algorithm for the discrete time nonlinear system with disturbances which produce two finite sequences of uniquely defined integers, the so-called invertibility indices, either with respect to control, or with respect to both inputs. The necessary and sufficient conditions for local solvability of the problem are derived in terms of the invertibility indices of the plant, the so-called extended system, formed from the plant and the model, and the so-called auxiliary system, formed from the plant. If these conditions are satisfied, the inversion algorithm provides a systematic procedure for constructing the precompensator that solves the problem.

Control 43/93Author(s): TAMM, Boris. Title: Elements of expert system technology. II. 61 p. Language: English Keywords:

ABSTRACT. This study is a continuation of the investigation presented in 1992 under the title "Elements of Expert System Technology". The study, carried out in this year (1993) is focused on knowledge processing methods using DFDs, ERDs, system shells, prototyping reasoning procedures and other techniques of modern structured analysis. It also emphasizes Prolog-oriented tools for designing user front-ends. Several particular inference mechanisms for reasoning processors are presented.

Control 44/93Author(s): VAIN, Jyri. Title: Compositional specification and verification of hybrid systems. 32 p. Language: English Keywords:

Control 45/93Author(s): KA"A"RAMEES, M., LITTOVER, M., RANDVEE, I., VAIN, J. Title: Towards integrated modelling techniques. 48 p. Language: English Keywords: ABSTRACT. Conceptual modelling of business processes at the initiation phase of the CIM project life cycle is investigated. The conceptual meta-model based on the open-EDI model and requirements specification language KAOS is elaborated and used as an intermediate specification language for requirements specification. The dimensions of metamodelling frame work are outlined. The class structure and intensional definitions for concepts used in software specifications are derived and concept operations analysed. An implementation example of derived concept classes in NUT language is also given.

Control 46/94Author(s): KOTTA, Ylle. Title: Discrete-time models of a nonlinear continuous-time system. 24 p. Language: English Keywords: Nonlinear system; sampled-data system; digital control. ABSTRACT. The paper studies the problem of sampling the multi-input analytic nonlinear continuous-time (CT) system. It derives the exact as well as the order approximate (with respect to sampling period T) discrete-time step-invariant model of CT system.

Control 47/94Author(s): KOTTA, Y., NIJMEIJER, H. Title: Immersion a discrete-time nonlinear system by regular dynamic state feedback into a linear system. 43 p. Language: English ABSTRACT. This paper studies the problem of immersion an analytic discrete-time nonlinear system by regular dynamic state feedback into a linear system. Necessary and sufficient conditions for local solvability of this problem around a given trajectory are obtained. The proposed conditions are less restrictive than those obtained by Lee and Marcus for the problem of immersion a nonlinear system into a linear system via a static state feedback. Instrumental in the problem solution is the inversion (structure) algorithm for discrete-time nonlinear system. The solvability conditions are expressed in terms of the inversion algorithm. Moreover, the construction of the both the dynamic state feedback and immersion map relies on this algorithm. Finally, it is shown that for locally right invertible systems, the considered problem, unlike the problem of immersion via static state feedback, is always solvable.

Control 48/94Author(s): KOTTA, Y. Title: Robust output tracking design for affine nonlinear system via variable structure control. 14 p. Language: English ABSTRACT. In this paper a robust output tracking design for affine nonlinear system via a variable structure controller is proposed. The considered systems are assumed to be invertible. The inversion algorithm is used to design a sliding manifold and propose the less stringent matching conditions for perturbations than those often used in connection with robust tracking.

Control 49/94Author(s): ARANDA-BRICAIRE, E., KOTTA, Y., MOOG, C. Title: A linear algebraic framework for feedback linearization of discrete-time nonlinear systems. 6 p. Language: English Keywords: Nonlinear systems; discrete-time systems; feedback; linearization techniques, algebraicmethods. ABSTRACT. The algebraic formalism developed in this paper unifies the study of two notions of linearizability for nonlinear discrete-time systems. The static state feedback linearization problem for discrete-time systems is recasted through the language of differential forms. This allows to give a solution which is completely constructive. The problem of the dynamic feedback linearization problem for discrete-time systems has never been addressed in the literature. We tackle it within the same formalism.

Control 50/94Author(s): NURGES, Ylo. Title: Robust stability of discrete-time controller. 7 p. Language: English ABSTRACT. By the use of a multilinear transform on coefficients space of closed loop characteristic polynomial a family of stable discrete-time systems are obtained starting from a nominal stable system. To find a polytopic family of stabilizable plants Kharitonov's weak theorem is used.

Control 51/94Author(s): NURGES, Ylo. Title: On the robust controller design via necessary stability conditions. 7 p. Language: English Keywords: Robust control; discrete-time systems; stability; polynomials; transfer functions. ABSTRACT. By the use of a multiparametric transform on coefficients space of closed loop characteristic polynomials a family of stable discrete-time systems is obtained starting from a nominal stable system. Only linear transforms have been used to formulate some necessary stability conditions and to introduce a rough stability measure. A straightforward robust controller design procedure is proposed for interval plant.

Control 52/94Author(s): ARANDA-BRICAIRE, E., KOTTA. Y., MOOG, C. H. Title: Accessibility and feedback linearization of discrete-time systems. 6 p. Language: Estonian ABSTRACT. The accessibility problem for nonlinear discrete-time systems is shown to be easy to tackle by means of standard linear algebraic tools whereas for nonlinear continous-time systems the most suitable approach is provided by differential geometry. The feedback linearization problem for discrete-time systems is recasted through the language of differential forms. This yields a solution which is completely constructive. In the event that a system is not feedback linearizable, the largest feedback linearizable subsystem is characterized within the same formalism using the notion of derived flag of a Pfaffian system.

Control 53/94Author(s): KOTTA, Y. Title: The effects of time-sampling on the solution of the nonlinear model matching problem. 66 p. Language: English Keywords: Nonlinear system; sampled-data system; digital control; model matching problem; approximation. ABSTRACT. The effects of time sampling on the strong model matching problem (SMMP) is considered. It is shown that the control objectives cannot be achieved even at given time instants when the control law, designed in the continuous-time (CT) domain, is discretized. The better approach is to obtain first an exact or higher order approximate (if compared to the Euler discretization scheme) discrete-time (DT) model of the CT system, and then to design a controller in the DT domain. It is shown that if the SMMP is solvable for CT system S and CT model M, then the corresponding sampled-data problem for exact DT models of S and M is also solvable. Moreover, it is shown, that if the relative degrees of the system are equal or greater than 2 then the multi-rate sampled-data (DT) models should be used in which the controls are sampled faster than the states and the outputs.

Control 54/94Author(s): KAARAMEES, M., , LITTOVER, M., RANDVEE, I., VAIN, J. Title: Functional meta-model of the business system. 59 p. Language: English ABSTRACT. A version of conceptual meta-model for Business Systems is derived. The meta-model is exposed inEntity-Attribute-Relationship terms. The main list of basic concepts is extracted from the conceptual views of a set of commonly known system design and specification methods. The object-oriented approach is adopted. The given version of conceptual meta-model is viewed as a near-natural language interface for the business system formalizers and for the user domain experts.

Control 55/94Author(s): HOOMAN, J., VAIN, J. Title: An integrated technique for developing real-time systems. 5 p. Language: English ABSTRACT. Integration of conceptual modelling and compositional specification and verification techniques for real-time systems is considered within the knowledge engineering context. Constructive transformations from a conceptual meta-model to the real-time specification language and specification rules for compositional refinement steps are defined. Applicability of the technique is evaluated on the mine pump control system derivation example.

Control 56/94Author(s): RIISMAA, T., VAIN, J. Title: Multi-level classification method for conceptual structures. 6 p. Language: English ABSTRACT. In this paper the optimization problem of inheritance trees of concept classes by multi-level classification method was considered. For that reason, inheritance trees of concept classes were parametrized and their optimality criteria defined. Using the notion of the conceptual space and Abstract parameters of inheritance trees the conceptual optimization task was mathematically stated and the applicability of the multi-level classification method demonstrated. Effectivity of the method was illustrated by a simple conceptual structurization example.

Control 57/94Author(s): KAARAMEES, M. Title: Transforming specifications: Step towards implementation. 5 p. Language: English

Control 58/94Title: Research, development and education programme for 1995-2000 on automatics and control systems (in Estonian) 17 p. Language: English

Control 59/94Author(s): HOOMAN, J., VAIN, J. Title: Compositional specification of control systems software. 34 p. Language: English ABSTRACT: In this report a specification and verification technique is proposed which is applicable in control software development process.

Control 60/94Author(s): TAMM, Boris. Title: Expert systems technology. 69 p. Language: English ABSTRACT. The first part of the study deals with modelling of a problem domain that does not fit usual fixed or probabilistic base structures and the knowledge must be derived and measured by some robust structures satisfying the expert reasoning. The second part discusses logical distances between the values of decision factors.

Control 61/95 Author(s): NURGES, Ylo.

Title: On the reflection coefficients and Schur stability. 8 p. Language: English Keywords: discrete-time systems; stability; polynomials Availability: ftp://ftp.ioc.ee/pub/reports/control/co61_95.ps.Z ABSTRACT. A useful Schur stability test by so-called reflection coefficients of a polynomial is recalled. Some simple necessary stability conditions in terms of unions of polytopes are obtained by splitting the unit hypercube of reflection coefficients and taking into account the multilinear dependency between the reflection coefficients and the coefficients of a polynomial.

Control 62/95 Author(s): NURGES, Ylo. Title: On the Schur stability and invariant transforms. 17 p., fig. Language: English Keywords: discrete-time systems; stability; polynomials Availability: ftp://ftp.ioc.ee/pub/reports/control/co62_95.ps.Z ABSTRACT. A useful Schur stability test by so-called reflection coefficients of the polynomials is recalled. A Schur invariant transform is introduced which preserves all the reflection coefficients inside the unit hypercube. Some simple necessary stability conditions in terms of unions of polytopes are obtained by splitting the unit hypercube of reflection coefficients. A rule for generating sufficient stability conditions in terms of simpleces is proposed using linear Schur invariant transforms.

Control 63/95 Author(s): ARANDA-BRICAIRE, E., KOTTA, Ylle. Title: Dynamic disturbance decoupling for discrete-time nonlinear systems: A linear algebraic solution. 6 p. Language: English Keywords: discrete-time systems; nonlinear control systems; disturbance decoupling; linear algebraic methods; dynamic state feedback; quasi-static state feedback Availability: ftp://ftp.ioc.ee/pub/reports/control/co63_95.ps.Z ABSTRACT. The paper presents a linear algebraic solution of the dynamic disturbance decoupling problem for a submersive discrete-time nonlinear system. The solution is looked for in the class of regular (invertible) dynamic compensators. Necessary and sufficient conditions in terms of certain subspaces , defined by the system, are given both for the cases of measurable and unmeasurable input disturbances. The linear algebraic solvability conditions are shown to be equivalent to the earlier conditions, formulated in terms of certain functions appearing in the inversion algorithm. The equivalence relies on the fact that two versions of the inversion algorithm for systems with disturbances produce the basis for the above subspaces. Moreover, we establish that when the disturbance decoupling problem is solvable by a dynamic state feedback, then it is solvable by a quasi-static state feedback.

Control 64/95 Author(s): FLIEGNER, Th., NIJMEIJER, H., KOTTA, Y. Title: On the solvability and right-inversion of implicit non-linear discrete-time systems. 6 p. Language: English Keywords: implicit non-linear discrete-time systems; solvability, right-inversion ABSTRACT. In this paper we review the problems of solvability and right invertibility for implicit non-linear discrete-time control systems. The concept 'solvability' is defined in such a way that consistency of the implicit system equations is locally guaranteed for all input sequences. In order to verify the solvability of an implicit system in that sense, we introduce the so -called shuffle algorithm. Finally it is shown how this mechanism can be used to decide on the right-invertibility of a given system and how to construct an inverse system

Control 65/95 Author(s): KOTTA, Ylle. Title: On right invertibility of nonlinear recursive systems. 14 p. Language: English Keywords: nonlinear recursive systems; delay orders; right inverti- bility Availability: ftp://ftp.ioc.ee/pub/reports/control/co65_95.ps.Z ABSTRACT. The right invertibility problem is studied for a class of recursive nonlinear systems (RNS), i. e. for systems, modelled by recursive nonlinear input-output equations involving only a finite

number of input values and a finite number of output values. The concept of delay orders and the special case of right invertibility, the notion of (d1, ...,dp)-forward time shift (FTS ) right invertibility, known for discrete-time nonlinear systems in state space from, are extended to RNS. Necessary and suffici- ent conditions for local (d1,.. .,dp)-FTS right invertibility are proposed. Finally, it is shown how to generalize the special case of right invertibility -(d1,..,dp)-FTS right invertibility- using the ideas from the statte space theory.

Control 66/95 Author(s): NURGES, Ylo. Title: On the Schur stability and robust control. Language: English Keywords: discrete-time systems; robust control; stability; poly- nomials; transfer functions Availability: ftp://ftp.ioc.ee/pub/reports/control/co66_95.ps.Z ABSTRACT. A useful Schur stability test by so-called reflection coefficients of the polynomial is recalled. A Schur invariant transform is introduced which preserves all the reflection coefficients inside the unit hypercube. Some simple necessary stability conditions in terms of unions of polytopes are obtained by splitting the unit hypercube of reflection coefficients. A rule for generating sufficient stability conditions in terms of simpleces is obtained using linear Schur invariant transforms. An heuristic procedure is proposed for robust controller design.

Control 67/95 Author(s): FLIEGNER, T., KOTTA, Y., NIJMEIJER, H. Title: Solvability and right-inversion of implicit nonlinear discrete-time systems. 26 p. Language: English Keywords: implicit nonlinear systems; solvability; right-invertibility ABSTRACT. In this paper the problems of solvability and right- invertibility for implicit nonlinear discrete-time control systems are investigated. The concept "solvability" is defined in such a way that consistency of the implicit system equations is locally guaranteed for all input sequences and an algorithm is introduced to verify the solvability of an implicit system in that sense. It is demonstrated how this mechanism may be used to decide on the right- invertibility of functional reproducibility of a given system. In contrast to previous work on right-invertibility for (special classes of) implicit nonlinear systems, the approach is not restricted to the characterization of right-invertibility but is shown in addition how an inverse system can actually be obtained. The theory is illustrated by realistic example in which the inversion procedure is applied using formula manipulation.

Control 68/95 Author(s): RIISMAA, Tiit, VAIN, Jyri. Title: Multi-level classification method of knowledge. 6 p. Language: English Keywords: class of concepts; inheritance tree; optimality of the inheritance tree Availability: ftp://ftp.ioc.ee/pub/reports/control/co68_95.ps.Z ABSTRACT. In this paper the multi-level classification method for conceptual structures is considered. This approach for describing and optimizing the structure of hierarchical systems is based on multi-level partitioning of the given finite set to subsets. The qualities of the system depend on this partitioning. The problem is to construct the hierarchical system of concepts with the minimal number of average comparisons needed for identifying the concepts of the lowest level. Thus, it is a nonlinear integer programming problem that is approximated with a continuous analogy and is solved analytically.

Control 69/95 Author(s): VAIN, J., KURKI-SUONIO, R. Title: Time-invariant transformations of joint action systems. 13 p., 2 fig. Language: English Keywords: joint action systems; timed model; transformations; static behavioural patterns; time-invariance Availability: ftp://ftp.ioc.ee/pub/reports/control/co69_95.ps.Z

Control 70/95 Author(s): HOOMAN, J., VAIN, J. Title: An integrated technique for developing real-time systems. 8 p.

Language: English Availability: ftp://ftp.ioc.ee/pub/reports/control/co70_95.ps.Z ABSTRACT. The integration of conceptual modelling techniques, formal specification, and compositional verification is considered for real-time systems within the knowledge engineering context. We define constructive transformations from a conceptual meta-model to a real-time specification language and give rules for compositional refinement steps. The ideas are illustrated by the design of a mine pump control system.

Control 71/95 Author(s): KA"A"RAMEES, Marko. Title: Transforming designs towards implementations. Language: English Keywords: reactive systems; safety critical systems; provable correct systems; refinement; specification transformation; Duration Calculus; DisCo ABSTRACT. We are interested in constructing safety-critical systems from their requirements specification. Our approach is the following: we start with requirements formalized in Duration Calculus (DC). These requirements are transformed to another form in DC, expressing the design of the system. The design is then transformed to a joint action system expressed in DisCo language. The specifications in DC emphasize properties the system must have, whereas the joint action system is closer to description how the system must be implemented. The philosophy is that all the involved transformations must be proven correct. This paper focuses on the transformation from a design in DC to a join action system in DisCo.

Control 72/95 Author(s): RANDVEE, I. Title: Events and links in scenario decomposition. 9 p. Language: English Keywords: requirements specification; behavior representation; events; actions Availability: ftp://ftp.ioc.ee/pub/reports/control/co72_95.Word.Z ABSTRACT. The role of an event in scenario decomposition is discussed. The event as an entity of its own right is introduced and the list of attributes is defined. Two oversimplified examples illustrate the main properties of events and links in decomposed scenario i.e. in the structuring of actions that the system will be expected to play.

Control 73/96Author(s): ARANDA-BRICAIRE, E., KOTTA, Ü., MOOG, C. H. Title: Linearization of discrete-time systems. 27 p. Language: English Keywords: nonlinear discrete-time systems * algebraic methods * accessibility * feedback linearization * differential forms * Pfaffian systems Availability: ftp://ftp.ioc.ee/pub/reports/control/co73_96.ps. ZABSTRACT.The algebraic formalism developed in this paper unifies the study of the accessibility problem and various notions of feedback linearizability for discrete-time nonlinear systems. The accessibility problem for nonlinear discrete-time systems is shown to be easy to tackle by means of standard linear algebraic tools whereas this is not the case for nonlinear continuous- time systems, in which case the most suitable approach is provided by differential geometry. The feedback linearization problem for discrete-time systems is recasted through the language of differential forms. In the event that a system is not feedback linearizable subsystem is characterized within the same formalism using the notion of derived flag of a Pfaffian system. A discrete-time system may be linearizable by dynamic state feedback though it is not linearizable by static state feedback. Necessary and sufficient conditions are given for the existence of a so-called linearizing output, which in turn is a sufficient condition for dynamic state feedback linearizability.

Control 74/96Author(s): ARANDA-BRICAIRE, E., KOTTA, Ü. Title: Generalized controlled invariance for discrete-time nonlinear systems with an application to the dynamic disturbance decoupling problem. 18 p. Language: English Availability: ftp://ftp.ioc.ee/pub/reports/control/co74_96.ps.Z

ABSTRACT. In analogy with the continuous-time case, a general notion of controlled invariance with respect to the quasi-static state feedback is introduced for discrete-time nonlinear systems which incorporates the earlier definition of controlled invariance with a respect to regular static state feedback. This new notion is shown to be applicable to derive a geometric solution to the dynamic disturbance decoupling problem. The proposed solution is a natural generalization of the geometric solution to the static disturbance decoupling problem.

Control 76/96Author(s): ARANDA-BRICAIRE, E., KOTTA, Ü. Title: Equivalence of discrete-time nonlinear systems to prime systems. 4 p. Language: English Availability: ftp://ftp.ioc.ee/pub/reports/control/co76_96.ps.Z

Control 77/96Author(s): KOTTA, Ü. Title: Nonlinear dynamic disturbance decoupling problem with partially measurable disturbances. 2 p. Language: English

Control 78/96Author(s): KOTTA, Ü. Title: Inversion algorithm for nonlinear recursive systems. 4 p. Language: English Availability: ftp://ftp.ioc.ee/pub/reports/control/co78_96.ps.Z

Control 78/96Author(s): KOTTA, Ü. Title: Inversion algorithm for nonlinear recursive systems. 4 p. Language: English Availability: ftp://ftp.ioc.ee/pub/reports/control/co78_96.ps.Z

Control 79/96Author(s): ARANDA-BRICAIRE, Eduardo, KOTTA, Ülle. Title: Equivalence of discrete-time nonlinear systems to prime systems. 8 p. Language: Estonian Availability: ftp://ftp.ioc.ee/pub/reports/control/co79_96.ps.Z ABSTRACT. Intrinsic necessary and sufficient conditions are obtained under which a discrete-time nonlinear system is equivalent to a prime system. The group of transformations that we consider includes (regular) static state feedback and both state space and output space diffeomorphisms.

Control 80/96Author(s): KOTTA, Ü., LIU, P., ZINOBER, A. Title: On realization of nonlinear systems described by higher-order difference equations. 2 p. Language: English Availability: ftp://ftp.ioc.ee/pub/reports/control/co79_96.ps.Z

Control 81/96Author(s): NURGES, Ülo. Title: Robust control via convex approximation of the stability region. 6 p. Language: English Keywords: robust stability * robust control * discrete-time systems Availability: ftp://ftp.ioc.ee/pub/reports/control/co81_96.ps.Z ABSTRACT. A Schur invariant transform on the coefficient space of polynomials is used to obtain a sufficient stability condition in shape of simplex. The order of polynomials could be increased step by step starting from some low order stable simplex. A stability measure is introduced as a minimal distance between the extreme points of interval system and the surface of the stable simplex. A straight-forward robust controller design procedure is proposed for interval plants. Some low order examples are given.

Control 82/96Author(s): NURGES, Ülo.

Title: A sufficient stability condition by Schur invariant transforms. 6 p. Language: English Availability: ftp://ftp.ioc.ee/pub/reports/control/co82_96.ps.Z ABSTRACT. Some inside approximations of the Schur stability region in polynomial coefficients space are given. A Schur invariant transform is introduced which preserves all the reflection coefficients of a polynomials inside the unit hypercube. A rule for generating sufficient stability conditions in terms of simpleces obtained using linear Schur invariant transforms.

Control 83/96Author(s): RIISMAA, T., RANDVEE, I. Title: Two-stage control scheme for reactive hybrid system. 6 p. Language: English Keywords: hybrid systems * control law implementation * structurization ABSTRACT. The second, control scenario implementation stage of two-stage control reactive hybrid systems (RHS) is considered. An optimal structure of the set of control modules is derived. The structure allows to select a control module and to generate sequences of control actions at time-critical operational stage as a reaction to periodically appearing sensor readings with minimal number of comparisons. In the first part of the paper a very general framework for RHS two-stage control is introduced. The second part is devoted to the representation of the main result.

Control 84/96Author(s): RANDVEE, I. Title: About the hybrid systems view. 8 p. (In Estonian). Language: Estonian Keywords: classification * mathematical models * hybrid systemsSUMMARY. The position of hybrid systems among the variety of mathematical models of all other control systems is discussed. In the first section the classification of control systems seen from the standpoint of engineer is introduced. The second section discusses the hybrid systems view through implementation independent characteristic entities such as: scenario, role, action, state and event interpreted in continuous and discrete domains. Some difficulties are outlined. It is well-known that control problems with constraint posed on state and output variables are hard to handle. In hybrid systems these constraints are strengthened by real- time restrictions. Third section gives one of possible definitions for hybrid control system. It is stressed that hybrid system is implemented as the interacting collection of analog and digital modules.

Control 85/96Author(s): RANDVEE, I. Title: Adaptive estimation scheme for linear interconnected subsystems.7 p. Language: English Keywords: decentralized estimation * parameter identification ABSTRACT. A decentralized state estimation schema for linear discrete-time systems is proposed. It is suited also for recursive correction of possible unknown parameters, located in subsystems. Whole procedure is based on repetitive real-time implementation of same Kalman filter algorithm.

Control 86/96Author(s): VAIN, Jüri, HOOMAN, Jozef. Title: Integrating methods for the design of real-time systems. 20 p. Language: English WK: conceptual modeling * formal specification * refinement *compositional verification * real-time ABSTRACT. With the aim of designing complex real-time systems, we investigate the integration of conceptual modeling techniques, formal specification, and compositional verification. A constructive transformation is defined from a conceptual meta-model to a real-time specification language. Refinement steps can be verified formally by means of compositional proof rules. The approach is illustrated by the design of a mine pump control system.

Control 87/96Author(s): KÄÄRAMEES, Marko, HANSEN, Michael R. Title: Transforming DC implementables into timed automata. 10 p. Language: English

Keywords: reactive systems * safety critical systems * provable correct systems * refinement * specification transformation * duration calculus *timed automata with deadlines ABSTRACT. We are interested in constructing safety-critical systems from their requirements formalized in Duration Calculus (DC). These requirements are refined to another form in DC, expressing the design of the system. The design is then transformed to Timed Automata with Deadlines (TAD). The philosophy is that all the involved transformations must be proven correct. This paper focuses on the transformation from a design in DC to TAD. We show in the paper how the transformation to TAD can be used for analyzing the consistency of the specification, simulating the design, and refining it towards the sequential implementation.

Control 88/96Author(s): MEISTER, E., EEK, A. Title: Estonian phonetics database: Development and realization. Language: English

Control 89/97Author(s): ARANDA-BRICAIRE, E., KOTTA, Ü. Title: The discrete-time nonlinear dynamic disturbance decoupling problem with partially mesurable disturbances. 4 p. Language: English ABSTRACT. The paper studies the discrete-time nonlinear dynamic disturbance decoupling problem with partially mesurable disturbances. The solution is formulated in terms of the notion of generalized controlled invariance with respect to the quasi-static state feedback which incorporates the earlier definition of controlled invariance with respect to the regular static state feedback. The propose solution is a natural generalization of the geometric solution of the static disturbance decoupling problem.

Control 90/97Author(s): KOTTA, Ü., LIU, P., ZINOBER, A. Title: Transfer equivalence of nonlinear higher order difference equations. 6 p. Language: English Keywords: nonlinear systems * discrete-time systems * input-output models * equivalence ABSTRACT. The problem of equivalence is considered for discrete- time nonlinear single-input single-output systems described by higher order input-output difference equations. A new definition of equivalence is introduced which generalizes the notion of transfer equivalence in the linear case. Our definition is based upon the notion of an irreducible differential form of the system and was inspired by the analogous definition for continuous time systems. Compared to the existing definition of equivalence of discrete-time nonlinear systems, it avoids many undesirable results.

Control 91/97Author(s): KOTTA, Ü., LIU, P., ZINOBER, A. Title: State-space realization of input-output nonlinear difference equations. 6 p. Language: English Keywords: nonlinear control * discrete-time systems ABSTRACT. The realization problem for single-input single-output discrete-time nonlinear systems is studied through the language of differential forms. Necessary and sufficient conditions are given for the existence of a (local) state-space realization of the input-output difference equation, i.e. a higher order difference equation in the input, the output and a finite number of their time-shifts. The sufficiency part of the proof gives a constructive procedure (up to the integration of one-forms) for obtaining a locally observable and accessible state-space system

Control 92/97Author(s): KOTTA, Ü. Title: Inversion algorithm for nonlinear recursive systems. 16 p. Language: English Keywords: nonlinear recursive systems * inversion algorithm * rank * right invertibility ABSTRACT. The right invertibility problem is studied for a class of recursive nonlinear systems (RNS), i.e. for systems, modelled by recursive nonlinear input-output equations involving only a finite number of input values and a finite number of output values. The concept of rank which plays the key role in the study of right invertibility for discrete-time nonlinear systems in state space form, is

extended to RNS. It is shown that the inversion algorithm provides the means to compute the rank of the system. Necessary and sufficient conditions for the local right invertibility in terms of the rank of the system are produced.

Control 93/97Author(s): KOTTA, Ü. Title: Lowering the orders of input shifts in discrete-time generalized state-space systems. 6 p. Language: English Keywords: nonlinear systems * discrete-time systems * generalized dynamics * generalized state transformations ABSTRACT. The problem of lowering the orders of input forward shifts in generalized state space systems by generalized state transformations is studied through the language of differential forms. Necessary and sufficient conditions are given for the local existence of such transformation. The sufficiency part of the proof gives a constructive procedure (up to the integration of one-forms) for finding these generalized state transformations. In particular case, these conditions show when it is possible to transform a generalized state space representation into the classical state equations.

Control 94/97Author(s): NURGES, Ü. Title: Discrete Kharitonov's theorem revisited. 10 p., 1 p. fig. Language: English Keywords: robust stability * discrete-time systems ABSTRACT. Starting from the discrete analog of weak Kharitonov's theorem for monic polynomials a sufficient stability condition in terms of polytopes is obtained by the use of a Schur invariant transformation on the polynomials coefficient space. This approach enables also to construct a stable n-dimensional simplex with all vertexes on the stability boundary

Control 95/97Author(s): NURGES, Ü. Title: Discrete Kharitonov's theorem and robust control. 12 p. Language: English Keywords: robust stability * discrete-time systems * robust control ABSTRACT. Starting from the discrete analog of weak Kharitonov's theorem for monic polynomials a sufficient stability condition in terms of a polytope is obtained by the use of a Schur invariant transformation in the polynomials coefficient space. This approach enables also to construct a stable n-dimensional simplex with all vertexes on the stability boundary. A straightforward robust controller design procedure is proposed for interval plants.

Control 96/97Title: Eesti keele foneetika: uuringud ja rakendused [Estonian fonetics: research and application] : Aruanne 1997 / E.Meister A.Eek, M.Rohtla, P.Tatter, M.Muskat, H.Saarts. (In Estonian). Language: Estonian

Control 97/97Author(s): RIISMAA, Tiit, RANDVEE, Ingmar. Title: Restructurization of control scenarios. 5 p. Language: English Keywords: hybrid control * general framework * set structure * optimization ABSTRACT. The second, control scenario implementation stage of two-stage control of active cells (AC) as a certain class of embedded systems is considered. An optimal structure of the set of control activities derived. The structure allows to select a control activity and to generate sequences of control actions at time-critical operational stage as a reaction to periodically appearing sensor readings with minimal number of comparisons. The structurization of a set of activities is exposed as a finite step clustering algorithm, solving integer optimization problem. In the introductive part of the paper a very general framework for AC two-stage control is exposed. The second part is devoted to the representation of the main result.

Control 98/97Author(s): RANDVEE, Ingmar. Title: Subsystem formation in two-level control scheme. 5 p.

Language: English Keywords: decomposition-coordination * subproblem closeness ABSTRACT. The partitioning of a linear discrete-time control problem to subproblems is considered. A quantitative measure, Euclidean norm of a matrix for comparing possible subsystem structures is derived.

Control 99/97Author(s): HOOMAN, Josef, VAIN, Jüri. Title: Combining conceptual modeling and formal methods to design control systems. 10 p. Language: English ABSTRACT. This paper investigates the integration of conceptual modeling techniques, formal specification, and compositional verification. A transformation from a conceptual meta-model to real-time specification language is defined. It is demonstrated how refinement steps can be verified formally by means of compositional rules. The approach is illustrated by the development of a Drum Boiler control system.

Control 100/97Author(s): VAIN, Jüri. Title: Towards effective interpretation of many sorted interval logic formulas. 11 p. Language: English

Control 101/97Author(s): KÄÄRAMEES, Marko, HANSEN, Michael R. Title: From design formulas to parallel implementations. 10 p. Language: English ABSTRACT. In this paper we show how to construct a parallel implementation for a certain kind of design specifications [Rav95], whose formulas can define stability, framing, selection, and progress properties. The implementation is described as a parallel composition of timed automata with deadlines [SiY96], where one automaton can read clocks of the other automata in the parallel composition. The class of timed automata is closed under this parallel composition. The relationship between the design specifications of [Rav95] and timed automata is also investigated in [Lak96]. The constructions presented in [Lak96] result in one timed automaton, whereas our transformation will give a parallel implementation.

Control 102/97Author(s): KÄÄRAMEES, Marko. Title: Comparison of hybrid automata. 4 p. Language: English

Control 103/98Author(s): KOTTA, Ü., TÕNSO, M. Title: Modeling of nonlinear control systems using Mathematica: first experiences. 5 p., 32 p. appendixes. (in Estonian). Language: Estonian

Control 104/98 Author(s): KOTTA, Ü. Title: State-space realization of nonlinear input-output difference equations. 8 p. Language: English

Control 105/98 Author(s): NURGES, Ü. Title: On the nice stability and reflection coefficients. 15 p. Language: English Keywords: robust control * pole placement * discrete-time systems ABSTRACT. A robust version of the robust controller design for discrete-time systems is introduced. Instead of a single stable point a stable simplex must be preselected in the closed loop characteristic polynomials coefficients space . A constructive procedure for generating simplexes inside the "nice stability region" is given starting from the unit hypercube of reflection coefficients of monic polynomials. This procedure is quite straightforward because, first, n edges are generated by a

linear Schur invariant transformation and, second, the most critical edge is determined by the difference of reflection coefficients numbers. The procedure of robust controller design makes use of a stability measure defined as the minimal distance between a preselected stable simplex and vertices of a uncertain polytopic plant.

Control 106/98Author(s): RANDVEE, I. Title: On the robustness of the control systems. 7 p. (in Estonian). Language: Estonian ABSTRACT. The role of the main concepts of robust stability and robust control in the modern control theory is exposed. The presentation is based on the single-input single-output system transfer functions. The paper is aimed at serving as an introduction to the selected series of topics to be presented by different authors at the Control Systems Seminar on Robustness and Hybrid Systems.

Control 107/98Author(s): RANDVEE, I. Title: Decentralized control of acyclic linear systems. 6 p. Language: English ABSTRACT. In this communication the real-time control problem for serially connected linear subsystems with no decision-making priorities is revisited. It is supposed that every subsystem must have it's own local control loop and every subsystem has access to the full information about the own state and the state of all preceding subsystems. Two main cases are considered. First: the overall goal of the system is to minimize the sum of local goals. And the second: every subsystem minimizes it's own local goal independently from all other, so that in the whole system the Nash equilibrium is established.

Control 108/99 Author(s):RANDVEE, I. Title: An algorithm for nonclassical LQ-optimal control. 8 p.(in Estonian) Language: English ABSTRACT. In this communication the early short communication of the author on the incentive control given in the context of arbitrary desired trajectory is elaborated. It is shown that in the case of unidirectional interconnections the leader can establish in the whole system the desired trajectory only by properly chosen equivalent representation of his control law. Analogous problem has been treated in the papers of T.Basar and H.Selbuz [7] and B.Tolwinski [4] in the context of closed loop Stackelberg solution of two-person nonzero-sum dynamic games. In [4,7] conditions are obtained under which a one-step memory strategy of the leader forces the follower to a team-optimal solution. In the mentioned short communication [8] the leader is allowed to choose any desired trajectory of the whole system, including the team-optimal.

Control 109/99 Author(s):KOTTA, Ü., ZINOBER, A. S. I., LIU, P. Title: Transfer equivalence and realization of nonlinear higher order input-output difference equations. 29 lk. Language: English ABSTRACT. Two fundamental modeling problems in nonlinear discrete-time control systems are studied using the language of differential forms. The discrete-time nonlinear single-input single-output systems to be studied are described by input-output (i/o) difference equations, i.e. a higher order difference equation relating the input, the output and finite number of their time-shifts. A new definition of equivalence is introduced which generalizes the notion of transfer equivalence, well known for their linear case. Our definition is based upon the notion of an irreducible differential form of the system and was inspired by the analogous definition for continuous-time systems. The second problem to be addressed is the realization problem. The i/o difference equation is assumed to be in the irreducible form so that one can obtain a minimal realization, i.e., one which is accessible and observable. Necessary and sufficient conditions are given for the existence of a (local) state-space realization of the irreducible i/o/ difference equation. These conditions are formulated in terms of the integrability of certain subspaces of one-forms, classified according to their relative degree. The sufficiency part of the proof gives a constructive procedure (up to the integration of one-forms) for obtaining a locally observable and accessible state-space system. If the system is not in the irreducible form, one first has to apply the reduction procedure to transform the system into the irreducible form.

Finally, the feasibility of symbolic computation using Maple, is discussed. A set of procedures have been developed in Maple V to test if a given i/o difference equation is irreducible and realizable in the classical state space form. Besides the mathematical examples, one example of a real process, whose model is obtained via identification, is considered.

110/99 Component based development of hybrid control systems. 17 lk.

111A/99 A specification language for model checker GRA. 20 lk.

111B/99 Design of a model checker GRA. 20 lk.

112/99 Theories for verification of hybrid systems in PVS. 25 lk.

Control 113/2000 Author(s): RANDVEE, I. Title: Structural Description of Holonic Information and Control Systems. 25 p. Language:English Keywords:information/control systems ; structured description ; holonic representation ABSTRACT. In this report the conceptual model of holonic information and control system (ICS) as the model of emerging class of virtual systems is introduced. It is shown that the structure of ICS can be described using basic concepts of CIM-OSA, software specification techniques, and hybrid control systems. The incorporation of humans as abstract objects allows connect them with other objects and nondeterministic finite automata. Two submodels are added to the conventional approach: functional/domain model and holonic/computerization model. The introduction of first is caused by the necessity for structured methods (DFD technique, SADT diagrams) at domain or macro-level of modelling. The second submodel, called holonic/computerizational model is closely related to the "organization" entities, their responsibilities and authorities. Every entity/holon of an organization hierarchy must be optimized in terms of required capabilities and competencies. This model defines the structure of the ICS holarchy and describes the flow/streams of material, information, control/decisions, technical and intellectual support between holons. It is aimed at collecting and preparing the conceptual knowledge for the design of the ICS computer and communication networks.

114A/00 Vain, J. Comparison of models for hybrid dynamical systems, 10 p.

114B/00 Vain, J., Kääramees, M. Relating formalism for real time and hybrid systems, 11 p.

116/00 Tagamets, M.-A. Towards multi-level brain modeling (activity report 1997). 6 p.

Control 119/01 Author(s):RANDVEE, I. Title: A straightforward estimation algorithm of linear stochastic hybrid systems. 6 p. Language: English ABSTRACT. A theoretical background and some practical considerations concerning the state estimation of linear hybrid systems are exposed. The hybrid system is given as the set of constituting subsystems in which only one is currently active for some time period. The algorithm is based on a straightforward comparison of innovation sequences taken from a set of standard Kalman filters, each tuned to the one of possible constituting subsystem. It is shown that after some time steps it is possible to point to the currently active subsystem and obtain its best state estimation.

Control 120/02 Author(s):RANDVEE, I. Title: Optimal control of discrete-time nonlinear systems based on performance criteria partition. 8 p.Language: English ABSTRACT. A parametrisation approach which has been introduced at 1980 -s in the context of multilevel systems is revisited. It is suggested that the version of that optimization technique (which skip the introduction of costates and the solution of two-point boundary value problem) may be applicable in the numerical simulation of one-step ahead unconstrained model-predictive control strategies and other suboptimal real-time dynamic systems which use predicted closed-loop system trajectories. The representation is given in discrete-time setting using state-space models. ÜLEVAADE. Esitatakse tehnika optimeerimisülesannete lahendamiseks, mis sisalduvad ennustava

juhtimise algoritmis. Tehnika baseerub sihifunktsiooni dekomponeerimisel, mille tulemusena saadakse osaliselt tagasisidestatud regulaator. Regulaatori avatud ahelaga juhttoime komponenti täpsustatakse iteratiivselt, kasutades sihifunktsiooni parametriseerimist. Tehnika on rakendatav nii lineaarsetele kui ka eralduvate muutujatega mittelineaarsetele objektidele. Antud tehnika on oluliselt lihtsam klassikalisest lahendusskeemist kuna ei nõua kaasmuutujatega rajaülesannete lahendamist. See asjaolu võimaldab laiendada ennustava juhtimise rakendusala keerukamatele objektidele, sealhulgas ka mitme lokaalse regulaatoriga Nash-optimaalsetele süsteemidele.

Control 121/03Author(s): KOTTA, Ü., NÕMM, S., ZINOBER, A.S.I.Title: Classical state space realizability of input-output bilinear models. 27 p.Language: EnglishNotes: This is the longer version that contains the detailed proofs. We submitted the shorter version to the journal. ABSTRACT. This paper studies the realizability property of bilinear input-output (i/o) models in the classical state space form. Constraints on the parameters of the bilinear i/0 model are suggested that lead to realizable models. The complete list of 2nd and 3rd order realizable input-output bilinear models together with the corresponding state equations is given. In the general case some subclasses of realizable bilinear models together with their state-space realizations are presented, including the diagonal bilinear model and the special subclass of superdiagonal bilinear model.

Control 122/03Author(s): KOTTA, Ü., PAWLUSZEWICZ, E., NÕMM, S.Title: Reducibility and reduction of discrete-time nonlinear control systems: comparison of two approaches. 6 p.Language: English ABSTRACT. The problem of system reduction is studied for discrete-time nonlinear single-input single-output systems described by high order input-output (i/o) difference equations, that is, given the i/o equation, can one find a minimal representation which is equivalent to the original system with the order being as small as possible. Comparison of two notions of reducibility is provided. The reducibility properties addressed are both generalizations of the well-known notion on transfer equivalence to the case of nonlinear control systems. Two roles of transfer equivalence are covered by these extensions. The first is that of identity of the 0utputs for any fixed control sequence under zero initial conditions. The second role is that of pole/zero cancellation that may occur in the transfer function of equivalent systems. The relationship between two reducibility criteria related to two equivalence notions is examined and the reducibility criterion which extends pole/zero cancellation property is shown to be stronger. Finally, the computational aspects of system reduction are discussed.

Control 123/03Author(s): RANDVEE, I.Title: Towards hybrid predictive control. 5p.Language: English ABSTRACT. Recently researchers started dealing with a class of hybrid systems (HS) which can be treated as hierarchical systems constituted by dynamical components at the lower level and governed by the upper level logical (discrete) components. Both, the logical part of the HS and the continuous part have been successfully elaborated, but mostly under the assumption that the problems arising in counterpart are already solved or are easily solvable. Very rare are papers, which deal with HS in which the controls of dynamic part are optimal, and obtained using model predictive control (MPC) methods. This report suggests the usage in HS the difference equation models as a promising subclass of mixed logical dynamical (MLD) models together with MPC algorithms. The approach is mostly transparent in logic, dynamics, and constraints, and can be used in modeling of realistic HS.