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Source: alexandria.tue.nl
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Mon Mar 04, 2013 05:29:03 PM
Short Desciption:
Model predictive control for hybrid systems,” which was financially suppor- ...... predictive control of constrained PWA systems. Hybrid Systems:
Summary:
1 Introduction 13
1.1 Hybrid systems 13
1.2 Model predictive control . 19
1.3 Open problems in model predictive control of hybrid systems 23
1.4 Outline of the thesis . 25
1.5 Summary of publications . 31
1.6 Basic mathematical notation and definitions 33
2 Classical stability results revisited 37
2.1 Introduction 37
2.2 Lyapunov stability 38
2.3 Input-to-state stability 43
2.4 Input-to-state practical stability . 46
2.5 Conclusions 50
3 Stabilizing model predictive control of hybrid systems 51
3.1 Introduction 51
3.2 Setting up the MPC optimization problem . 52
3.3 Stabilization conditions for hybrid MPC 54
3.3.1 Main results 54
3.3.2 The class of PWA systems 57
3.3.3 The problem statement reconsidered 58
3.4 Computation of the terminal cost 59
3.4.1 Quadratic MPC costs 59
3.4.2 MPC costs based on 1,1-norms 64
3.5 Computation of the terminal set: Low complexity invariant
sets for PWA systems 67
3.5.1 Polyhedral invariant sets . 67
3.5.2 Squaring the circle 70
3.5.3 Norms as Lyapunov functions 82
3.6 Terminal equality constraint . 82
3.7 Illustrative examples . 85
2 Contents
3.7.1 Example 1 . 85
3.7.2 Example 2 . 87
3.7.3 Example 3 . 88
3.8 Conclusions 91
4 Global input-to-state stability and stabilization of discretetime
piecewise affine systems 93
4.1 Introduction 93
4.2 An example of zero robustness in PWA systems 97
4.3 Problem statement 101
4.4 Analysis 102
4.5 Synthesis . 106
4.6 Illustrative examples . 109
4.6.1 Example 1 . 109
4.6.2 Example 2 . 110
4.7 Concluding remarks . 113
5 Robust stabilization of discontinuous piecewise affine systems
using model predictive control 115
5.1 Introduction 115
5.2 Preliminaries . 117
5.3 A motivating example 120
5.4 A posteriori tests for checking robustness 123
5.5 Robust predictive controllers for discontinuous PWA systems 127
5.5.1 Input-to-state stabilizing MPC using tightened constraints
. 127
5.5.2 Dual-mode input-to-state stabilizing MPC . 130
5.6 Illustrative examples . 134
5.6.1 Example 1 . 134
5.6.2 Example 2 . 135
5.7 Conclusions 137
6 Input-to-state stabilizing min-max predictive controllers 139
6.1 Introduction 139
6.2 Min-max MPC: Problem set-up . 141
6.3 ISpS results for min-max nonlinear MPC 143
6.4 ISS results for min-max nonlinear MPC 146
6.5 New methods for computing the terminal cost . 151
6.5.1 Specific problem statement . 152
6.5.2 MPC costs based on quadratic forms 153
6.5.3 MPC costs based on 1,1-norms 156
Contents 3
6.6 Illustrative examples . 158
6.6.1 An active suspension system . 158
6.6.2 A perturbed double integrator 160
6.6.3 A perturbed nonlinear double integrator 162
6.7 Conclusions 166
7 Robust sub-optimal model predictive controllers 169
7.1 Introduction 169
7.2 Sub-optimal MPC algorithms for fast nonlinear systems . 171
7.2.1 A contraction approach . 172
7.2.2 An artificial Lyapunov function approach . 174
7.3 Application to PWA systems 177
7.4 Application to the control of DC-DC converters 181
7.5 Concluding remarks . 184
8 Conclusions 187
8.1 Contributions . 187
8.1.1 Stability Theory of Hybrid Systems . 187
8.1.2 Stabilizing Model Predictive Control 189
8.1.3 Robust Model Predictive Control 190
8.2 Ideas for future research . 193
8.2.1 Stability Theory of Hybrid Systems . 193
8.2.2 Set Invariance Theory 194
8.2.3 Robust Model Predictive Control 194
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"Model Predictive Control of Hybrid Systems: Stability and Robustness"
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