2.153 Adaptive Control Fall 2019 Lecture 1:...
23
2.153 Adaptive Control Fall 2019 Lecture 1: Introduction Anuradha Annaswamy [email protected] September 4, 2019 ( [email protected]) September 4, 2019 1 / 11
Transcript of 2.153 Adaptive Control Fall 2019 Lecture 1:...
2.153 Adaptive ControlFall 2019
Lecture 1: Introduction
Anuradha Annaswamy
September 4, 2019
( [email protected]) September 4, 2019 1 / 11
Adaptive Control
Adaptive Control, a thirty-year old field, is an advanced control method that isbecoming increasingly popular in various engineering applications. The ability toself-correct a controller in the presence of uncertainties using online information isits main and most compelling feature. This course will lay out the foundation ofadaptive control in continuous-time and discrete-time systems. Examples fromaerospace, propulsion, automotive, and energy systems will be used to elucidatethe underlying concepts.
( [email protected]) September 4, 2019 2 / 11
Definition of Adaptation
Biology: Advantageous Conformation of an Organism to Changes
Adaptive Control: The control of Uncertain Systems
Other Definitions:Truxal: An adaptive system is one designed from an adaptive viewpoint.
Zadeh: A is adaptive with respect to Sγ and Γ if it performs acceptablywell for every source in the family Sγ , γ ∈ Γ
( [email protected]) September 4, 2019 3 / 11
Definition of Adaptation
Biology: Advantageous Conformation of an Organism to Changes
Adaptive Control: The control of Uncertain Systems
Other Definitions:Truxal: An adaptive system is one designed from an adaptive viewpoint.
Zadeh: A is adaptive with respect to Sγ and Γ if it performs acceptablywell for every source in the family Sγ , γ ∈ Γ
( [email protected]) September 4, 2019 3 / 11
Definition of Adaptation
Biology: Advantageous Conformation of an Organism to Changes
Adaptive Control: The control of Uncertain Systems
Other Definitions:Truxal: An adaptive system is one designed from an adaptive viewpoint.
Zadeh: A is adaptive with respect to Sγ and Γ if it performs acceptablywell for every source in the family Sγ , γ ∈ Γ
( [email protected]) September 4, 2019 3 / 11
Definition of Adaptation
Biology: Advantageous Conformation of an Organism to Changes
Adaptive Control: The control of Uncertain Systems
Other Definitions:Truxal: An adaptive system is one designed from an adaptive viewpoint.
Zadeh: A is adaptive with respect to Sγ and Γ if it performs acceptablywell for every source in the family Sγ , γ ∈ Γ
( [email protected]) September 4, 2019 3 / 11
Definition of Adaptation (contd.)
Bellman:
Deterministic System: When the controller has complete informationabout the behavior of the inputs, and the system is completely specified.
Stochastic system: When unknown factors are present in the system whichappear mathematically as random variables with knwon distributionfunctions
Adaptive system: Even less is known about the system and the controllerhas to learn to improve its performance through the observation of theoutputs of the system as it evolves.
In this course:Adaptive Control: The control of plants with unknown parameters
( [email protected]) September 4, 2019 4 / 11
Definition of Adaptation (contd.)
Bellman:
Deterministic System: When the controller has complete informationabout the behavior of the inputs, and the system is completely specified.
Stochastic system: When unknown factors are present in the system whichappear mathematically as random variables with knwon distributionfunctions
Adaptive system: Even less is known about the system and the controllerhas to learn to improve its performance through the observation of theoutputs of the system as it evolves.
In this course:Adaptive Control: The control of plants with unknown parameters
( [email protected]) September 4, 2019 4 / 11
Control System
Open-loop Dynamic System
Feedback Control System
Performance Measures: Stability, speed, accuracy
( [email protected]) September 4, 2019 5 / 11
Control System
Open-loop Dynamic System Feedback Control System
Performance Measures: Stability, speed, accuracy
( [email protected]) September 4, 2019 5 / 11
Adaptive Control System
In the presence of uncertainties, using prior and on-line information, thecontroller adapts itself.
( [email protected]) September 4, 2019 6 / 11
History
Adaptive systems
Caught the imagination in the 60’s
Several symposia - to define adaptation
First use in flight control
Hypersonics program - highly successful
Five classes of adaptive systems
Passive Adaptation
Input Signal Adaptation
System variable adaptation
System characteristic adaptation
Extremum adaptation
( [email protected]) September 4, 2019 7 / 11
History
Adaptive systems
Caught the imagination in the 60’s
Several symposia - to define adaptation
First use in flight control
Hypersonics program - highly successful
Five classes of adaptive systems
Passive Adaptation
Input Signal Adaptation
System variable adaptation
System characteristic adaptation
Extremum adaptation
( [email protected]) September 4, 2019 7 / 11
Adaptive Control: A Parametric Framework
Nonlinear, time-varying, with unknown parameter θ
x = f(x, u, θ, t) y = h(x, u, θ, t)
Nonlinear, with unknown parameter θ
x = f(x, u, θ) y = h(x, u, θ)
Linear Time-Varying (LTV) with unknown parameter θ
x = A(θ, t)x+B(θ, t)u y = C(θ, t)x+D(θ, t)u
Linear Time-Invariant (LTI) with unknown parameter θ
x = A(θ)x+B(θ)u y = C(θ)x+D(θ)u
Adapt to the unknown parameter
( [email protected]) September 4, 2019 8 / 11
Adaptive Control: A Parametric Framework
Nonlinear, time-varying, with unknown parameter θ
x = f(x, u, θ, t) y = h(x, u, θ, t)
Nonlinear, with unknown parameter θ
x = f(x, u, θ) y = h(x, u, θ)
Linear Time-Varying (LTV) with unknown parameter θ
x = A(θ, t)x+B(θ, t)u y = C(θ, t)x+D(θ, t)u
Linear Time-Invariant (LTI) with unknown parameter θ
x = A(θ)x+B(θ)u y = C(θ)x+D(θ)u
Adapt to the unknown parameter
( [email protected]) September 4, 2019 8 / 11
Direct and Indirect Adaptive Control
θp: Plant parameter - unknown; θc: Control parameter
Indirect Adaptive Control: Estimate θp as θp. Compute θc using θp.Also known as Explicit EstimationDirect Adaptive Control: Directly estimate θc as θc. Compute the plantestimate θp using θcAlso known as Implicit Estimation
( [email protected]) September 4, 2019 9 / 11
Parametric Adaptation
Parameter perturbation methods
http://flyingv.ucsd.edu/krstic/talks/ExtremumSeeking.pdf
Sensitivity methods
( [email protected]) September 4, 2019 10 / 11
In this course
Many of our discussions will involve
Control designs motivated by linear design methods
Parametrizations of the control structure
Parameter adjustment rules - Adaptive laws
What to measure?What to adjust? How many parameters?How often?How do we adjust?
A Stability Framework
( [email protected]) September 4, 2019 11 / 11
In this course
Many of our discussions will involve
Control designs motivated by linear design methods
Parametrizations of the control structure
Parameter adjustment rules - Adaptive laws
What to measure?What to adjust? How many parameters?How often?How do we adjust?
A Stability Framework
( [email protected]) September 4, 2019 11 / 11
In this course
Many of our discussions will involve
Control designs motivated by linear design methods
Parametrizations of the control structure
Parameter adjustment rules - Adaptive laws
What to measure?What to adjust? How many parameters?How often?How do we adjust?
A Stability Framework
( [email protected]) September 4, 2019 11 / 11
In this course
Many of our discussions will involve
Control designs motivated by linear design methods
Parametrizations of the control structure
Parameter adjustment rules - Adaptive laws
What to measure?What to adjust? How many parameters?How often?How do we adjust?
A Stability Framework
( [email protected]) September 4, 2019 11 / 11
In this course
Many of our discussions will involve
Control designs motivated by linear design methods
Parametrizations of the control structure
Parameter adjustment rules - Adaptive laws
What to measure?What to adjust? How many parameters?How often?How do we adjust?
A Stability Framework
( [email protected]) September 4, 2019 11 / 11
In this course
Many of our discussions will involve
Control designs motivated by linear design methods
Parametrizations of the control structure
Parameter adjustment rules - Adaptive laws
What to measure?What to adjust? How many parameters?How often?How do we adjust?
A Stability Framework
( [email protected]) September 4, 2019 11 / 11
