Robust Control Design Using H Methods

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Format: Hardcover
Pub. Date: 2000-10-01
Publisher(s): Springer Verlag
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Summary

This book provides a unified collection of important, recent results for the design of robust controllers for uncertain systems. Most of the results presented are based on H? control theory, or its stochastic counterpart, risk sensitive control theory.Central to the philosophy of the book is the notion of an uncertain system. Uncertain systems are considered using several different uncertainty modeling schemes. These include norm bounded uncertainty, integral quadratic constraint (IQC) uncertainty and a number of stochastic uncertainty descriptions. In particular, the authors examine stochastic uncertain systems in which the uncertainty is outlined by a stochastic version of the IQC uncertainty description.For each class of uncertain systems covered in the book, corresponding robust control problems are defined and solutions discussed.

Table of Contents

Frequently used notation xv
Introduction
1(18)
The concept of an uncertain system
1(4)
Overview of the book
5(14)
Uncertain systems
19(36)
Introduction
19(1)
Uncertain systems with norm-bounded uncertainty
20(2)
Special case: sector-bounded nonlinearities
20(2)
Uncertain systems with integral quadratic constraints
22(8)
Integral quadratic constraints
22(3)
Integral quadratic constraints with weighting coefficients
25(1)
Integral uncertainty constraints for nonlinear uncertain systems
26(1)
Averaged integral uncertainty constraints
27(3)
Stochastic uncertain systems
30(25)
Stochastic uncertain systems with multiplicative noise
31(5)
Stochastic uncertain systems with additive noise: Finite-horizon relative entropy constraints
36(8)
Stochastic uncertain systems with additive noise: Infinite-horizon relative entropy constraints
44(11)
H∞ control and related preliminary results
55(48)
Riccati equations
55(6)
H∞ control
61(20)
The standard H∞ control problem
63(11)
H∞ control with transients
74(5)
H∞ control of time-varying systems
79(2)
Risk-sensitive control
81(13)
Exponential-of-integral cost analysis
82(3)
Finite-horizon risk-sensitive control
85(4)
Infinite-horizon risk-sensitive control
89(5)
Quadratic stability
94(1)
A connection between H∞ control and the absolute stabilizability of uncertain systems
95(8)
Definitions
96(2)
The equivalence between absolute stabilization and H∞ control
98(5)
The S-procedure
103(22)
Introduction
103(2)
An S-procedure result for a quadratic functional and one quadratic constraint
105(5)
Proof of Theorem
106(4)
An S-procedure result for a quadratic functional and k quadratic constraints
110(4)
An S-procedure result for nonlinear functionals
114(7)
An S-procedure result for averaged sequences
121(1)
An S-procedure result for probability measures with constrained relative entropies
121(4)
Guaranteed cost control of time-invariant uncertain systems
125(56)
Introduction
125(2)
Optimal guaranteed cost control for uncertain linear systems with norm-bounded uncertainty
127(10)
Quadratic guaranteed cost control
127(2)
Optimal controller design
129(6)
Illustrative example
135(2)
State-feedback minimax optimal control of uncertain systems with structured uncertainty
137(18)
Definitions
138(3)
Construction of a guaranteed cost controller
141(10)
Illustrative example
151(4)
Output-feedback minimax optimal control of uncertain systems with unstructured uncertainty
155(13)
Definitions
155(2)
A necessary and sufficient condition for guaranteed cost stabilizability
157(3)
Optimizing the guaranteed cost bound
160(4)
Illustrative example
164(4)
Guaranteed cost control via a Lyapunov function of the Lur'e-Postnikov form
168(11)
Problem formulation
168(4)
Controller synthesis via a Lyapunov function of the Lur'e-Postnikov form
172(5)
Illustrative Example
177(2)
Conclusions
179(2)
Finite-horizon guaranteed cost control
181(34)
Introduction
181(1)
The uncertainty averaging approach to state-feedback minimax optimal control
182(11)
Problem statement
182(3)
A necessary and sufficient condition for the existence of a state-feedback guaranteed cost controller
185(8)
The uncertainty averaging approach to output-feedback optimal guaranteed cost control
193(7)
Problem statement
193(2)
A necessary and sufficient condition for the existence of a guaranteed cost controller
195(5)
Robust control with a terminal state constraint
200(8)
Problem statement
200(2)
A criterion for robust controllability with respect to a terminal state constraint
202(3)
Illustrative example
205(3)
Robust control with rejection of harmonic disturbances
208(6)
Problem statement
208(2)
Design of a robust controller with harmonic disturbance rejection
210(4)
Conclusions
214(1)
Absolute stability, absolute stabilization and structured dissipativity
215(30)
Introduction
215(2)
Robust stabilization with a Lyapunov function of the Lur'e-Post-nikov form
217(13)
Problem statement
217(1)
Design of a robustly stabilizing controller
218(12)
Structured dissipativity and absolute stability for nonlinear uncertain systems
230(13)
Preliminary remarks
230(1)
Definitions
231(2)
A connection between dissipativity and structured dissipativity
233(4)
Absolute stability for nonlinear uncertain systems
237(6)
Conclusions
243(2)
Robust control of stochastic uncertain systems
245(102)
Introduction
245(2)
H∞ control of stochastic systems with multiplicative noise
247(29)
A stochastic differential game
249(16)
Stochastic H∞ control with complete state measurements
265(8)
Illustrative example
273(3)
Absolute stabilization and minimax optimal control of stochastic uncertain systems with multiplicative noise
276(14)
The stochastic guaranteed cost control problem
276(4)
Stochastic absolute stabilization
280(5)
State-feedback minimax optimal control
285(5)
Output-feedback finite-horizon minimax optimal control of stochastic uncertain systems with additive noise
290(17)
Definitions
290(4)
Finite-horizon minimax optimal control with stochastic uncertainity constraints
294(6)
Design of a finite-horizon minimax optimal controller
300(7)
Output-feedback infinite-horizon minimax optimal control of stochastic uncertain systems with additive noise
307(37)
Definitions
307(3)
Absolute stability and absolute stabilizability
310(6)
A connection between risk-sensitive optimal control and minimax optimal control
316(14)
Design of the infinite-horizon minimax optimal controller
330(8)
Connection to H∞ control
338(1)
Illustrative example
339(5)
Conclusions
344(3)
Nonlinear versus linear control
347(46)
Introduction
347(1)
Nonlinear versus linear control in the absolute stabilizability of uncertain systems with structured uncertainty
348(13)
Problem statement
348(3)
Output-feedback nonlinear versus linear control
351(10)
State-feedback nonlinear versus linear control
361(1)
Decentralized robust state-feedback H∞ control for uncertain large-scale systems
361(14)
Preliminary remarks
361(3)
Uncertain large-scale systems
364(3)
Decentralized controller design
367(8)
Nonlinear versus linear control in the robust stabilizability of linear uncertain systems via a fixed-order output-feedback controller
375(8)
Definitions
375(3)
Design of a fixed-order output-feedback controller
378(5)
Simultaneous H∞ control of a finite collection of linear plants with a single nonlinear digital controller
383(9)
Problem statement
383(1)
The design of a digital output-feedback controller
384(8)
Conclusions
392(1)
Missile autopilot design via minimax optimal control of stochastic uncertain systems
393(10)
Introduction
393(1)
Missile autopilot model
394(5)
Uncertain system model
395(4)
Robust controller design
399(2)
State-feedback controller design
399(1)
Output-feedback controller design
399(2)
Conclusions
401(2)
Robust control of acoustic noise in a duct via minimax optimal LQG control
403(16)
Introduction
403(1)
Experimental setup and modeling
404(4)
Experimental setup
404(1)
System identification and nominal modelling
405(1)
Uncertainty modelling
405(3)
Controller design
408(6)
Experimental results
414(3)
Conclusions
417(2)
A. Basic duality relationships for relative entropy 419(2)
B. Metrically transitive transformations 421(6)
References 427(22)
Index 449

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