Efficient Software Tools for Control and Analysis of Hybrid Systems

Acknowledgement......Page 7
Abstract......Page 9
Zusammenfassung......Page 11
Contents......Page 13
NOTATION......Page 21
INTRODUCTION......Page 25
BACKGROUND......Page 29
Standard Optimization Problems......Page 31
Definitions......Page 35
Operations on Polytopes......Page 38
Operations on P-collections......Page 43
Definitions......Page 49
Properties and Computation......Page 51
Efficient Polytope Reduction in Multi-Parametric Programming......Page 55
Detecting Non-Redundant Half-Spaces......Page 56
Detecting Redundant Half-Spaces......Page 58
Complete Algorithm......Page 59
Other Usage of Bounding Boxes......Page 60
Numerical Examples......Page 62
Constrained Finite-Time Optimal Control (CFTOC)......Page 65
Receding Horizon Control......Page 67
EFFICIENT CONTROL OF PWA SYSTEMS......Page 71
Introduction......Page 73
Background and Definitions......Page 74
Construction of Stabilizing Controllers for Piecewise Affine Systems......Page 79
Low Complexity Feedback Control of Piecewise Affine Systems......Page 83
Minimum-Time Controller......Page 84
Minimum-Time Controller: Off-Line Computation......Page 85
Minimum-Time Controller: On-Line Application......Page 88
Reduced Switching Controller......Page 90
M-step Controller......Page 92
Stability Analysis......Page 93
M-step Controller Computation......Page 96
Numerical Examples......Page 98
Conclusion......Page 102
Efficient Evaluation of Piecewise Control Laws defined over a Large Number of Polyhedra......Page 105
Point Location Problem......Page 106
Alternative Search Approaches......Page 107
The Proposed Search Algorithm......Page 110
Bounding Box Search Tree......Page 111
Preprocessing......Page 113
Constrained LTI System......Page 114
Constrained PWA System......Page 116
Ball & Plate System......Page 118
Conclusion......Page 121
THE MULTI PARAMETRIC TOOLBOX......Page 123
Introduction......Page 125
LTI Dynamics......Page 129
PWA Dynamics......Page 130
Import of Models from External Sources......Page 132
Constraints on System Outputs......Page 133
Constraints on Slew Rate of Manipulated Variables......Page 134
Mixed Inputs......Page 135
LTI systems......Page 136
PWA Systems......Page 138
Mixed Logical Dynamical Systems......Page 141
HYSDEL......Page 142
Vector and Matrix Variables......Page 143
Vector and Matrix Parameters......Page 144
Indexing of Vectors and Matrices......Page 145
Loops......Page 147
Nested Loops......Page 149
Vector Functions......Page 150
Import of Models Generated by HYSDEL and matrixHYSDEL into MPT......Page 151
Controller Computation......Page 153
Fields of the mptctrl object......Page 155
Design Phase......Page 156
Computation Phase......Page 157
Soft Constraints......Page 162
Control of Time-Varying Systems......Page 163
On-line MPC for Nonlinear Systems......Page 164
One and Infinity Norm Problems......Page 165
Quadratic Cost Problems......Page 166
Level of Optimality......Page 167
Optional Fields......Page 168
Reachability Computation......Page 171
Verification......Page 174
Complexity Reduction......Page 176
Evaluation of Explicit Control Laws......Page 179
Implementation......Page 181
Using different dynamical system in sim and simplot......Page 183
Export of Controllers to C-code......Page 184
Export of Search Trees to C-code......Page 185
Plotting of Polyhedral Partitions......Page 187
Visualization of Closed-loop and Open-loop Trajectories......Page 188
Visualization of General PWA and PWQ Functions......Page 189
Examples......Page 191
Creating a Polytope......Page 195
Accessing Data Stored in a Polytope Object......Page 196
Polytope Arrays......Page 199
Geometric Operations on Polytopes......Page 200
Hybrid Toolbox......Page 205
User Interface......Page 206
Provided Functionality......Page 208
Simulink Integration......Page 209
Testing Methodology and Numerical Results......Page 210
Discussion......Page 211
Future Development......Page 217
Improved Export of Controllers to C-code......Page 219
Re-design of Controller Objects......Page 220
New Object Representing Functions Defined over Polytopes......Page 221
Main Goals for HYSDEL......Page 223
CASE STUDIES......Page 225
Introduction......Page 227
Optimal Infusion Policy of Intravenous Morphine and Ketamine......Page 229
The model......Page 230
The Optimal Control Problem......Page 232
The Control Problem......Page 235
Discussion......Page 237
Conclusion......Page 240
Erratum (after publication of the thesis)......Page 241
Introduction......Page 243
Mechanical System with Backlash......Page 244
Modeling of Hybrid Systems......Page 245
Backlash Model......Page 246
Parameter Identification......Page 249
State Estimation......Page 250
Validation......Page 252
Model Predictive Control for constrained linear and PWA systems......Page 253
MPC design for mechanical system with backlash......Page 255
Comparison of different control strategies......Page 256
Conclusion......Page 261
APPENDIX......Page 263
System dynamics......Page 265
matrixHYSDEL model......Page 266
AMPL model......Page 268
System dynamics......Page 273
matrixHYSDEL model......Page 274
AMPL model......Page 277
Curriculum Vitae......Page 283
Publication List......Page 285
Bibliography......Page 287