Model Predictive Control

Contents ix
12.5 State Feedback Solution, 1-Norm and ∞-Norm Case . . . . . . . . . 255
12.6 Parametrizations of the Control Policies . . . . . . . . . . . . . . . . 260
12.7 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263
12.8 Robust Receding Horizon Control . . . . . . . . . . . . . . . . . . . . 264
12.9 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266
13 On-line Control Computation 267
13.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268
13.2 Efficient On-Line Algorithms . . . . . . . . . . . . . . . . . . . . . . 269
13.3 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278
13.4 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279
V Constrained Optimal Control of Hybrid Systems 281
14 Models of Hybrid Systems 283
14.1 Hybrid models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283
14.2 Piecewise Affine Systems . . . . . . . . . . . . . . . . . . . . . . . . . 284
14.3 Discrete Hybrid Automata . . . . . . . . . . . . . . . . . . . . . . . . 291
14.4 Logic and Mixed-Integer Inequalities . . . . . . . . . . . . . . . . . . 296
14.5 Mixed Logical Dynamical Systems . . . . . . . . . . . . . . . . . . . 299
14.6 Model Equivalence . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300
14.7 The HYSDEL Modeling Language . . . . . . . . . . . . . . . . . . . 301
14.8 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306
15 Optimal Control of Hybrid Systems 311
15.1 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 312
15.2 Properties of the State Feedback Solution, 2-Norm Case . . . . . . . 314
15.3 Properties of the State Feedback Solution, 1, ∞-Norm Case . . . . . 321
15.4 Computation of the Optimal Control Input via Mixed Integer Programming322
15.5 State Feedback Solution via Batch Approach . . . . . . . . . . . . . 324
15.6 State Feedback Solution via Recursive Approach . . . . . . . . . . . 325
15.7 Discontinuous PWA systems . . . . . . . . . . . . . . . . . . . . . . . 334
15.8 Receding Horizon Control . . . . . . . . . . . . . . . . . . . . . . . . 335
Bibliography 341