2.153 adaptive control spring 2015 lecture 0 1-246mzqu.mit.edu/material/lect/lecture0.pdf ·...

2.153 Adaptive ControlSpring 2015

Lecture 01-246

Anuradha Annaswamy

aanna@mit.edu

( aanna@mit.edu ) 1 / 13

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.

The midterm will be assigned towards the end of March, and will be an openbook exam.

Grade distribution: Homework: 20%; Midterm: 40%; Project: 40%

Textbook: Stable Adaptive Systems, K.S. Narendra and A.M. Annaswamy, DoverPublications, 2004.

Additional notes will be distributed throughout the semester.Daily class notes will be available at: http://aaclab.mit.edu/material.php

( aanna@mit.edu ) 2 / 13

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.

The midterm will be assigned towards the end of March, and will be an openbook exam.

Grade distribution: Homework: 20%; Midterm: 40%; Project: 40%

Textbook: Stable Adaptive Systems, K.S. Narendra and A.M. Annaswamy, DoverPublications, 2004.

Additional notes will be distributed throughout the semester.Daily class notes will be available at: http://aaclab.mit.edu/material.php

( aanna@mit.edu ) 2 / 13

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.

The midterm will be assigned towards the end of March, and will be an openbook exam.

Grade distribution: Homework: 20%; Midterm: 40%; Project: 40%

Textbook: Stable Adaptive Systems, K.S. Narendra and A.M. Annaswamy, DoverPublications, 2004.

Additional notes will be distributed throughout the semester.Daily class notes will be available at: http://aaclab.mit.edu/material.php

( aanna@mit.edu ) 2 / 13

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.

The midterm will be assigned towards the end of March, and will be an openbook exam.

Grade distribution: Homework: 20%; Midterm: 40%; Project: 40%

Textbook: Stable Adaptive Systems, K.S. Narendra and A.M. Annaswamy, DoverPublications, 2004.

Additional notes will be distributed throughout the semester.Daily class notes will be available at: http://aaclab.mit.edu/material.php

( aanna@mit.edu ) 2 / 13

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.

The midterm will be assigned towards the end of March, and will be an openbook exam.

Grade distribution: Homework: 20%; Midterm: 40%; Project: 40%

Textbook: Stable Adaptive Systems, K.S. Narendra and A.M. Annaswamy, DoverPublications, 2004.

Additional notes will be distributed throughout the semester.Daily class notes will be available at: http://aaclab.mit.edu/material.php

( aanna@mit.edu ) 2 / 13

TOC

Lecture # Topic Date0 Introduction Feb 4

1 Adaptive Identification - Error Model 1 Feb 92 Adaptive Control - Error Model 3 Feb 11

3 Adaptive Control - Scalar Case Feb 174 Stability Theory Feb 18

5 Closed-loop Reference Models Feb 236 States Accessible: SISO Plants Feb 25

7 States Accessible: MIMO Plants March 28 Adaptive PI Control March 4

9 Adaptive PID Control March 910 Adaptive Phase Lead Compensators March 11

( aanna@mit.edu ) 3 / 13

TOC

Lecture # Topic Date11 Uniform Asymptotic Stability and Persistent Excitation March 1612 Review: Stability, Asymptotic Stability March 18

13 Persistent Excitation and Adaptive Observers March 3014 Adaptive Control - n∗ = 1 April 1

15 Adaptive Control - n∗ = 1 April 616 Adaptive Control - n∗ ≥ 2 April 8

17 Adaptive Control - n∗ ≥ 2 April 1318 Robust Adaptive Control - Disturbances April 15

19 Robust Adaptve Control -Time-varying Parameters April 2220 Robust Adaptve Control - Unmodeled Dynamics April 2721 High Order Tuners April 2922 Back stepping methods May 423 Adaptive Systems with Saturation May 624 Project presentations May 1125 Project presentations May 13

( aanna@mit.edu ) 4 / 13

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

( aanna@mit.edu ) 5 / 13

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

( aanna@mit.edu ) 5 / 13

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

( aanna@mit.edu ) 5 / 13

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

( aanna@mit.edu ) 5 / 13

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

( aanna@mit.edu ) 6 / 13

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

( aanna@mit.edu ) 6 / 13

Control System

Open-loop Dynamic System

Feedback Control System

Performance Measures: Stability, speed, accuracy

( aanna@mit.edu ) 7 / 13

Control System

Open-loop Dynamic System Feedback Control System

Performance Measures: Stability, speed, accuracy

( aanna@mit.edu ) 7 / 13

Adaptive Control System

In the presence of uncertainties, using prior and on-line information, thecontroller adapts itself.

( aanna@mit.edu ) 8 / 13

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

( aanna@mit.edu ) 9 / 13

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

( aanna@mit.edu ) 9 / 13

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

( aanna@mit.edu ) 10 / 13

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

( aanna@mit.edu ) 10 / 13

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

( aanna@mit.edu ) 11 / 13

Parametric Adaptation

Parameter perturbation methods

Sensitivity methods

( aanna@mit.edu ) 12 / 13

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

( aanna@mit.edu ) 13 / 13

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

( aanna@mit.edu ) 13 / 13

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

( aanna@mit.edu ) 13 / 13

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

( aanna@mit.edu ) 13 / 13

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

( aanna@mit.edu ) 13 / 13

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

( aanna@mit.edu ) 13 / 13