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.- 2.3 Uncertain systems with integral quadratic constraints.- 2.4 Stochastic uncertain systems.- 3. H? control and related preliminary results.- 3.1 Riccati equations.- 3.2 H? control.- 3.3 Risk-sensitive control.- 3.4 Quadratic stability.- 3.5 A connection between H? control and the absolute stabilizability of uncertain systems.- 4. The S-procedure.- 4.1 Introduction.- 4.2 An S-procedure result for a quadratic functional and one quadratic constraint.- 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.- 5.3 State-feedback minimax optimal control of uncertain systems with structured uncertainty.- 5.4 Output-feedback minimax optimal control of uncertain systems with unstructured uncertainty.- 5.5 Guaranteed cost control via a Lyapunov function of the Lur’e-Postnikov form.- 5.6 Conclusions.- 6. Finite-horizon guaranteed cost control.- 6.1 Introduction.- 6.2 The uncertainty averaging approach to state-feedback minimax optimal control.- 6.3 The uncertainty averaging approach to output-feedback optimal guaranteed cost control.- 6.4 Robust control with a terminal state constraint.- 6.5 Robust control with rejection of harmonic disturbances.- 7. Absolute stability, absolute stabilization andstructured dissipativity.- 7.1 Introduction.- 7.2 Robust stabilization with a Lyapunov function of the Lur’e-Postnikov form.- 7.3 Structured dissipativity and 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.- 8.3 Absolute stabilization and minimax optimal control of stochastic uncertain systems with multiplicative noise.- 8.4 Output-feedback finite-horizon minimax optimal control of stochastic uncertain systems with additive noise.- 8.5 Output-feedback infinite-horizon minimax optimal control of stochastic uncertain systems with additive noise.- 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.- 9.3 Decentralized robust state-feedback H? control for uncertain large-scale systems.- 9.4 Nonlinear versus linear control in the robust stabilizability of linear uncertain systems via a fixed-order output-feedback controller.- 9.5 Simultaneous H? control of a finite collection of linear plants with a single nonlinear digital controller.- 9.6 Conclusions.- 10. Missile autopilot design via minimax optimal control of stochastic uncertain systems.- 10.1 Introduction.- 10.2 Missile autopilot model.- 10.3 Robust 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.- 11.3 Controller design.- 11.4 Experimental results.- 11.5 Conclusions.- A. Basic duality relationships for relative entropy.- B. Metrically transitive transformations.- References.
