Dynamical Networks: Structural Analysis and Synthesis · UNIVERSITÀ DEGLI STUDI DI UDINE –...
Transcript of Dynamical Networks: Structural Analysis and Synthesis · UNIVERSITÀ DEGLI STUDI DI UDINE –...
UNIVERSITÀ DEGLI STUDI DI UDINE – Dottorato di Ingegneria Industriale e dell’Informazione www.uniud.it
PhD student: Giulia Giordano Supervisor: Prof. Franco Blanchini
social networks
production anddistribution systems
(bio)chemicalprocesses
A B C
synchronization
telecommunication / data communication networks
water distribution networks
traffic managementbiological systems, ecosystems
DYNAMICAL NETWORKS:structural analysis
and synthesis
UNIVERSITÀ DEGLI STUDI DI UDINE – Dottorato di Ingegneria Industriale e dell’Informazione www.uniud.it
Dynamical network:subsystems (each with its own dynamics)interconnected by "flows" / interactions
(hyper-)graph representation:nodes→subsystems
arcs→flows
social networks
production anddistribution systems
(bio)chemicalprocesses
A B C
synchronization
telecommunication / data communication networks
water distribution networks
traffic managementbiological systems, ecosystems
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UNIVERSITÀ DEGLI STUDI DI UDINE – Dottorato di Ingegneria Industriale e dell’Informazione www.uniud.it
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Compartmental systems...
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...generalised
graphrepresentation:nodes→compartmentsarcs→flows
hyper-graph:flows can requireinteractions amongmore than twocompartments
- positive systems- “mass” conservation constraints- flow: interaction between two compartments
UNIVERSITÀ DEGLI STUDI DI UDINE – Dottorato di Ingegneria Industriale e dell’Informazione www.uniud.it
A twofold goal
Structural Analysis
...especially meant for...
Structural Control Synthesis
- independent of parameters- based on the nature of interactions (graph topology)- explain robustness and characteristic behaviours
- interactions decided based onlocal information (decentralized)- control / coordinate global system behaviour
Natural Systems Man-made Systems
biologically-inspired design: learn from nature
synthetic biology:engineer natural systems
→ Applications tobiochemical systems
→ Network-decentralized control
UNIVERSITÀ DEGLI STUDI DI UDINE – Dottorato di Ingegneria Industriale e dell’Informazione www.uniud.it
Structural Analysis
Structural Control Synthesis
→Applications to biochemical systems
UNIVERSITÀ DEGLI STUDI DI UDINE – Dottorato di Ingegneria Industriale e dell’Informazione www.uniud.it
explain behavioursbased on the system
inherent structure
Biological systems are extremely robust:fundamental properties are preserved
despite huge uncertainties and parameter variations
structure graph
STRUCTURAL ANALYSIS
(...motifs...)
Structural property:satisfied by all the systems of a family
specified by a structure without numerical bounds
UNIVERSITÀ DEGLI STUDI DI UDINE – Dottorato di Ingegneria Industriale e dell’Informazione www.uniud.it
stability boundedness
Yes
No
Yes
No
Numerical tests based on polyhedral Lyapunov functionsto structurally assess
F. Blanchini, G. Giordano,“Piecewise-linear Lyapunov functions for structural stability of biochemical networks”, Automatica
UNIVERSITÀ DEGLI STUDI DI UDINE – Dottorato di Ingegneria Industriale e dell’Informazione www.uniud.it
Structural graph-based classificationof oscillatory/multistationary behaviours
F. Blanchini, E. Franco, G. Giordano,“A structural classification of candidate oscillators and multistationary systems”, Bull. Math. Biol.
Candidate oscillator
Candidate multistable
UNIVERSITÀ DEGLI STUDI DI UDINE – Dottorato di Ingegneria Industriale e dell’Informazione www.uniud.it
Similar results hold for the interconnectionof structurally stable monotone subsystems
F. Blanchini, E. Franco, G. Giordano,“Structural conditions for oscillations and multistationarity in aggregate monotone systems”, submitted
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SSMS
SSMS
SSMS SSMS
SSMS
SSMS
Candidate oscillator
Candidate multistable
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UNIVERSITÀ DEGLI STUDI DI UDINE – Dottorato di Ingegneria Industriale e dell’Informazione www.uniud.it
F. Blanchini, C. Cuba Samaniego, E. Franco, G. Giordano,“Design of a molecular clock with RNA–mediated regulation”, IEEE CDC 2014
x1 z1z3
e2 e1
r2 , e1 , q1
r1 , e2 , q2
z1 , z2 , x3
x1 , x2 , z3
Negative feedback of
two monotone subsystems
Synthesis of biomolecular oscillators
UNIVERSITÀ DEGLI STUDI DI UDINE – Dottorato di Ingegneria Industriale e dell’Informazione www.uniud.it
Structural steady-state analysis
Increase Decrease
Perfect adaptation
Depends on parameters
G. Giordano, C. Cuba Samaniego, E. Franco, F. Blanchini,“Computing the Structural Influence Matrix for Biological Systems”, submitted
Input variationOutput variation(at steady state)
UNIVERSITÀ DEGLI STUDI DI UDINE – Dottorato di Ingegneria Industriale e dell’Informazione www.uniud.it
G. Giordano, C. Cuba Samaniego, E. Franco, F. Blanchini,“Computing the Structural Influence Matrix for Biological Systems”, submitted
Influence matrix:structural steady-state variation of variable i
due to a persistent additive input applied to variable j
Network fromShinar&Feinberg (2010)
Structural steady-state analysis
UNIVERSITÀ DEGLI STUDI DI UDINE – Dottorato di Ingegneria Industriale e dell’Informazione www.uniud.it
Structural Analysis
Structural Control Synthesis
→Network-decentralized control
UNIVERSITÀ DEGLI STUDI DI UDINE – Dottorato di Ingegneria Industriale e dell’Informazione www.uniud.it
huge number of subsystems
subsystemscontrolagents
UNIVERSITÀ DEGLI STUDI DI UDINE – Dottorato di Ingegneria Industriale e dell’Informazione www.uniud.it
Control strategy decided locally,to govern the dynamics of the whole system
The feedback matrix has a structure given by the graph
F. Blanchini, E. Franco, G. Giordano, “Structured–LMI Conditions for Stabilizing Network–Decentralized Control”,IEEE CDC13; “Network-Decentralized Control Strategies for Stabilization”, IEEE Trans. Autom. Contr.
UNIVERSITÀ DEGLI STUDI DI UDINE – Dottorato di Ingegneria Industriale e dell’Informazione www.uniud.it
Node traffic splitting
Internal node dynamics: stochastic Markov matrix
Network-decentralized control:- robust (independent of Markov coefficients)- optimal: minimum norm (fairness)
F. Blanchini, G. Giordano, P. L. Montessoro,“Network–decentralized robust congestion control with node traffic splitting”, IEEE CDC 2014
UNIVERSITÀ DEGLI STUDI DI UDINE – Dottorato di Ingegneria Industriale e dell’Informazione www.uniud.it
PhD results: publicationsJournal papers
* F. Blanchini, E. Franco, G. Giordano, “Network-Decentralized Control Strategies for Stabilization”, IEEE Trans. on Autom. Control, Feb. 2015.* F. Blanchini, G. Giordano, “Piecewise-linear Lyapunov Functions for Structural Stability of Biochemical Networks”, Automatica, Oct. 2014.* F. Blanchini, E. Franco, G. Giordano, “A Structural Classification of Candidate Oscillatory and Multistationary Biochemical Systems”, Bulletin of Mathematical Biology, Oct. 2014.
Conference papers (peer reviewed)* F. Blanchini, G. Fenu, G. Giordano, F. A. Pellegrino, “Inverse Kinematics by Means of Convex Programming: Some Developments”, IEEE CASE, Gothenburg, August 2015.* F. Blanchini, D. Casagrande, G. Giordano, U. Viaro, “Properties of Switching–Dynamics Race Models”, ECC, Linz, July 2015.* F. Blanchini, G. Giordano, “Structural Stability of Biochemical Networks: Quadratic vs. Polyhedral Lyapunov Functions”, ROCOND, Bratislava, July 2015.* F. Blanchini, G. Giordano, P. L. Montessoro, “Network–Decentralized Robust Congestion Control with Node Traffic Splitting”, IEEE CDC, Los Angeles, December 2014.* F. Blanchini, C. Cuba Samaniego, E. Franco, G. Giordano, “Design of a Molecular Clock with RNA–mediated Regulation”, IEEE CDC, Los Angeles, December 2014.* F. Blanchini, E. Franco, G. Giordano, “Structured-LMI Conditions for Stabilizing Network-Decentralized Control”, IEEE CDC, Firenze, December 2013.
UNIVERSITÀ DEGLI STUDI DI UDINE – Dottorato di Ingegneria Industriale e dell’Informazione www.uniud.it
Gantt chartAttività / Mese 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
Analisi bibliografia e letteratura
Analisi teorica / Simulaz numeriche
Periodi all'estero
Articoli scientifici e conferenze CD
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ACC
CDC
Attività formativa scientifica
Corsi formativi complementari
Prep conferenze di dottorato
Preparazione relazioni annuali
Stesura della tesi
Journal/Conference paper
Presentation & Poster
Annual report
PhD thesis
Visits abroad: (1) Supélec, FR, 7-10 April 2014; (2) INP Grenoble, FR, 14-16 May 2014; (3) UC Riverside, CA, USA, December 2014; (4) Universität Stuttgart, DE, March-May 2015.
Papers: (1) Proc. ACC 2013; (2) Proc. CDC 2013; (3) ACS Synthetic Biology; (4) Automatica + Bull Math Biol; (5) Proc. CDC 2014; (6) IEEE Trans Autom Contr; (7) Proc. ROCOND + Proc. ECC 2015.
Training: (1) Photovoltaics: Principles and Devices; (2) Analisi Numerica IV; (3) Metodi topologiciper la ricerca di punti fissi; (4) Scuola Nazionale di Dottorato SIDRA 2013; (5) InterdisciplinaryPhD Spring School; (6) Corso di Deontologia e Pratica Professionale; (7) Lyapunov methodsfor robustness of control systems, PhD School, Grenoble; (8) Il ruolo del ricercatore in Europa;(9) Seminars in Stuttgart; (10) Set theoretic Fault Tolerant Control, Summer School, Grenoble
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UNIVERSITÀ DEGLI STUDI DI UDINE – Dottorato di Ingegneria Industriale e dell’Informazione www.uniud.it
PhD Thesis: Contents (tentative)DYNAMICAL NETWORKS: STRUCTURAL ANALYSIS AND SYNTHESISAbstract1 Introduction2 Structural PropertiesI Background on Dynamical NetworksII Structural Analysis of Dynamical Networks3 Structural Stability and Boundedness4 Structural Classification of Oscillatory and Multistationary Systems5 Structural Steady-State Analysis and Influence Matrix6 How Structural Analysis Can Aid the Synthesis of Biochemical Systems6.1 Design of Biomolecular Oscillators6.2 Rate Regulation in Artificial Gene NetworksIII Structural Control Synthesis for Dynamical Networks7 Network-Decentralized Control Strategies for Stabilization8 Network-Decentralized Congestion Control with Node Traffic Splitting8.1 A Robust Decentralized Control for Channel-Sharing Communication9 Compartmental Flow Control: Decentralization, Robustness and Optimality***10 Conclusions and OutlookIV AppendixBibliography
UNIVERSITÀ DEGLI STUDI DI UDINE – Dottorato di Ingegneria Industriale e dell’Informazione www.uniud.it
GRAZIE!
...and still a lot of interesting work to do !
Conclusions
☻
Now there is a PhD thesis to write...
☻