Optimal Control of Constrained Piecewise Affine Systems

PREFACE......Page 7
CONTENTS......Page 12
1.1 Set Terminology......Page 26
1.2 Polyhedra......Page 30
1.3 Function Terminology......Page 35
1.4 Constrained Optimization......Page 37
1.5 Multi-Parametric Programming......Page 40
2.1 Systems Formulation......Page 43
2.2 Invariance and Stability......Page 44
3
RECEDING HORIZON CONTROL......Page 49
3.1 Basic Idea......Page 50
3.2 Closed-form Solution to Receding Horizon Control......Page 51
3.3 Choice of the Cost Function......Page 55
3.4 Stability and Feasibility in Receding Horizon Control......Page 58
4
PIECEWISE AFFINE SYSTEMS......Page 62
4.1 Obtaining a PWA Model......Page 64
5
INTRODUCTION......Page 66
5.1 Software Implementation......Page 68
6
CONSTRAINED FINITE TIME
OPTIMAL CONTROL......Page 69
6.1 CFTOC Solution via mp-MILP......Page 72
6.2 CFTOC Solution via Dynamic Programming......Page 74
6.3 An Ef.cient Algorithm for the CFTOC Solution......Page 75
6.4 Comments on the Dynamic Programming Approach for the CFTOC Problem......Page 77
6.5 Receding Horizon Control......Page 79
6.6 Examples......Page 80
7.1 Problem Formulation......Page 85
7.2 Closed-loop Stability of the CITOC Solution......Page 87
7.3 CITOC Solution via Dynamic Programming......Page 89
7.4 An Ef.cient Algorithm for the CITOC Solution......Page 101
7.5 Examples......Page 107
8.1 Introduction......Page 113
8.3 Stability Theory for Linear Systems Using Linear Vector Norms......Page 115
8.4 Complex......Page 116
8.5 Construction of a Real......Page 117
8.6 Simple Algebraic Test to Substitute the Feasibility LP......Page 124
8.7 Computational Complexity and Finite Termination......Page 125
8.9 Guaranteeing Exponential Stability in Receding Horizon Control for Piecewise Af.ne Systems......Page 128
8.10 Examples......Page 130
9.1 Introduction......Page 132
9.2 Constrained Finite Time Optimal Control of Piecewise Af.ne Systems......Page 133
9.3 Closed-Loop Stability and Feasibility......Page 134
9.4 Examples......Page 146
10.1 Introduction......Page 153
10.2 Constrained Finite Time Optimal Control of Piecewise Af.ne Systems......Page 154
10.3 Stability Tubes for Nonlinear Systems......Page 157
10.4 Computation of Stability Tubes for Piecewise Af.ne Systems......Page 161
10.5 Comments on Stability Tubes......Page 162
10.6 Examples......Page 165
11.1 Introduction......Page 168
11.2 Software Implementation......Page 169
11.4 Constrained Finite Time Optimal Control of Piecewise Af.ne Systems......Page 170
11.5 Alternative Search Approaches......Page 172
11.6 The Proposed Search Algorithm......Page 174
11.7 Complexity......Page 177
11.8 Examples......Page 178
APPENDIX......Page 184
BIBLIOGRAPHY......Page 186
AUTHOR INDEX......Page 197
INDEX......Page 201