This is a unified collection of important recent results for the design of robust controllers for uncertain systems, primarily based on H8 control theory or its stochastic counterpart, risk sensitive control theory. Two practical applications are used to illustrate the methods throughout.
1. Introduction.- 1.1 The concept of an uncertain system.- 1.2 Overview of the book.- 2. Uncertain systems.- 2.1 Introduction.- 2.2 Uncertain systems with norm-bounded uncertainty.- 2.2.1 Special case: sector-bounded nonlinearities.- 2.3 Uncertain systems with integral quadratic constraints.- 2.3.1 Integral quadratic constraints.- 2.3.2 Integral quadratic constraints with weighting coefficients.- 2.3.3 Integral uncertainty constraints for nonlinear uncertain systems.- 2.3.4 Averaged integral uncertainty constraints.- 2.4 Stochastic uncertain systems.- 2.4.1 Stochastic uncertain systems with multiplicative noise.- 2.4.2 Stochastic uncertain systems with additive noise: Finitehorizon relative entropy constraints.- 2.4.3 Stochastic uncertain systems with additive noise: Infinite-horizon relative entropy constraints.- 3. H? control and related preliminary results.- 3.1 Riccati equations.- 3.2 H? control.- 3.2.1 The standard H? control problem.- 3.2.2 H? control with transients.- 3.2.3 H? control of time-varying systems.- 3.3 Risk-sensitive control.- 3.3.1 Exponential-of-integral cost analysis.- 3.3.2 Finite-horizon risk-sensitive control.- 3.3.3 Infinite-horizon risk-sensitive control.- 3.4 Quadratic stability.- 3.5 A connection between H? control and the absolute stabilizability of uncertain systems.- 3.5.1 Definitions.- 3.5.2 The equivalence between absolute stabilization and H? control.- 4. The S-procedure.- 4.1 Introduction.- 4.2 An S-procedure result for a quadratic functional and one quadratic constraint.- 4.2.1 Proof of Theorem 4.2.1.- 4.3 An S-procedure result for a quadratic functional and k quadratic constraints.- 4.4 An S-procedure result for nonlinear functionals.- 4.5 An S-procedure result for averaged sequences.- 4.6 An S-procedure result for probability measures with constrained relative entropies.- 5. Guaranteed cost control of time-invariant uncertain systems.- 5.1 Introduction.- 5.2 Optimal guaranteed cost control for uncertain linear systems with norm-bounded uncertainty.- 5.2.1 Quadratic guaranteed cost control.- 5.2.2 Optimal controller design.- 5.2.3 Illustrative example.- 5.3 State-feedback minimax optimal control of uncertain systems with structured uncertainty.- 5.3.1 Definitions.- 5.3.2 Construction of a guaranteed cost controller.- 5.3.3 Illustrative example.- 5.4 Output-feedback minimax optimal control of uncertain systems with unstructured uncertainty.- 5.4.1 Definitions.- 5.4.2 A necessary and sufficient condition for guaranteed cost stabilizability.- 5.4.3 Optimizing the guaranteed cost bound.- 5.4.4 Illustrative example.- 5.5 Guaranteed cost control via a Lyapunov function of the Lur’e-Postnikov form.- 5.5.1 Problem formulation.- 5.5.2 Controller synthesis via a Lyapunov function of the Lur’e-Postnikov form.- 5.5.3 Illustrative Example.- 5.6 Conclusions.- 6. Finite-horizon guaranteed cost control.- 6.1 Introduction.- 6.2 The uncertainty averaging approach to state-feedback minimax optimal control.- 6.2.1 Problem Statement.- 6.2.2 A necessary and sufficient condition for the existence of a state-feedback guaranteed cost controller.- 6.3 The uncertainty averaging approach to output-feedback optimal guaranteed cost control.- 6.3.1 Problem statement.- 6.3.2 A necessary and sufficient condition for the existence of a guaranteed cost controller.- 6.4 Robust control with a terminal state constraint.- 6.4.1 Problem Statement.- 6.4.2 A criterion for robust controllability with respect to a terminal state constraint.- 6.4.3 Illustrative example.- 6.5 Robust control with rejection of harmonic disturbances.- 6.5.1 Problem Statement.- 6.5.2 Design of a robust controller with harmonic disturbance rejection.- 6.6 Conclusions.- 7. Absolute stability, absolute stabilization and structured dissipativity.- 7.1 Introduction.- 7.2 Robust stabilization with a Lyapunov function of the Lur’e-Postnikov form.- 7.2.1 Problem statement.- 7.2.2 Design of a robustly stabilizing controller.- 7.3 Structured dissipativity and absolute stability for nonlinear uncertain systems.- 7.3.1 Preliminary remarks.- 7.3.2 Definitions.- 7.3.3 A connection between dissipativity and structured dissipativity.- 7.3.4 Absolute stability for nonlinear uncertain systems.- 7.4 Conclusions.- 8. Robust control of stochastic uncertain systems.- 8.1 Introduction.- 8.2 H? control of stochastic systems with multiplicative noise.- 8.2.1 A stochastic differential game.- 8.2.2 Stochastic H? control with complete state measurements.- 8.2.3 Illustrative example.- 8.3 Absolute stabilization and minimax optimal control of stochastic uncertain systems with multiplicative noise.- 8.3.1 The stochastic guaranteed cost control problem.- 8.3.2 Stochastic absolute stabilization.- 8.3.3 State-feedback minimax optimal control.- 8.4 Output-feedback finite-horizon minimax optimal control of stochastic uncertain systems with additive noise.- 8.4.1 Definitions.- 8.4.2 Finite-horizon minimax optimal control with stochastic uncertainty constraints.- 8.4.3 Design of a finite-horizon minimax optimal controller.- 8.5 Output-feedback infinite-horizon minimax optimal control of stochastic uncertain systems with additive noise.- 8.5.1 Definitions.- 8.5.2 Absolute stability and absolute stabilizability.- 8.5.3 A connection between risk-sensitive optimal control and minimax optimal control.- 8.5.4 Design of the infinite-horizon minimax optimal controller.- 8.5.5 Connection to H? control.- 8.5.6 Illustrative example.- 8.6 Conclusions.- 9. Nonlinear versus linear control.- 9.1 Introduction.- 9.2 Nonlinear versus linear control in the absolute stabilizability of uncertain systems with structured uncertainty.- 9.2.1 Problem statement.- 9.2.2 Output-feedback nonlinear versus linear control.- 9.2.3 State-feedback nonlinear versus linear control.- 9.3 Decentralized robust state-feedback H? control for uncertain large-scale systems.- 9.3.1 Preliminary remarks.- 9.3.2 Uncertain large-scale systems.- 9.3.3 Decentralized controller design.- 9.4 Nonlinear versus linear control in the robust stabilizability of linear uncertain systems via a fixed-order output-feedback controller.- 9.4.1 Definitions.- 9.4.2 Design of a fixed-order output-feedback controller.- 9.5 Simultaneous H? control of a finite collection of linear plants with a single nonlinear digital controller.- 9.5.1 Problem statement.- 9.5.2 The design of a digital output-feedback controller.- 9.6 Conclusions.- 10. Missile autopilot design via minimax optimal control of stochastic uncertain systems.- 10.1 Introduction.- 10.2 Missile autopilot model.- 10.2.1 Uncertain system model.- 10.3 Robust controller design.- 10.3.1 State-feedback controller design.- 10.3.2 Output-feedback controller design.- 10.4 Conclusions.- 11. Robust control of acoustic noise in a duct via minimax optimal LQG control.- 11.1 Introduction.- 11.2 Experimental setup and modeling.- 11.2.1 Experimental setup.- 11.2.2 System identification and nominal modelling.- 11.2.3 Uncertainty modelling.- 11.3 Controller design.- 11.4 Experimental results.- 11.5 Conclusions.- A. Basic duality relationships for relative entropy.- B. Metrically transitive transformations.- References.
