Preface 5
1. Control of systems 7
1.1 Preliminary 7
1.2 Mathematical modeling 7
1.3 General properties of control systems 9
1.3.1 Definitions 9
1.3.2 Attainability relation 11
1.3.3 Linear systems 12
1.3.4 Controllability 14
1.4 Optimal control and related results 15
1.4.1 Optimal control 15
1.4.2 The existence of optimal control 17
1.4.3. Invariant sets 19
1.4.4 Stability of invariant sets 20
1.4.5 Attractors and repellers 21
1.4.6 Attracting, repelling and saddle holding sets 22
1.4.7 Periodic orbits 23
2. Global optimal methods 25
2.1 The Hamilton-Jacobi theory 25
2.1.1 Introduction 25
2.1.2 Global sufficient conditions 26
2.2 The LQ problem 27
2.2.1 Introduction 27
2.2.2 Finite control horizon 28
2.2.3 Infinite control horizon 33
2.2.4 Optimal regulator 34
2.2.4.1 Stability properties 41
2.2.4.2 Robustness properties 45
2.2.4.3 The cheap control 46
2.2.4.4 The inverse problem 47
2.3 LQG problem 50
2.3.1 Introduction 50
2.3.2 Kalman filter 51
2.3.2.1 Nominal case 52
2.3.2.2 Singular case 57
2.3.3 LQG control problem 59
2.3.3.1 Finite control horizon 60
2.3.3.2 Infinite control horizon 61
3. Robust optimal control 65
3.1 ? ? Optimal Control: Riccati-Approach 65
3.1.1 Introduction 65
3.1.2 Formulation of the general ? H problem 65
3.1.3 Characterization of ? H suboptimal controllers
by means of Riccati equations 66
3.1.3.1 Characterization theorem for output feedback 66
3.1.3.2 Outline of the proof 67
References 69

Optimal control

Издания