Preface......Page 7
Contents......Page 12
1.1.1 Models......Page 17
1.1.2 Control Objectives......Page 18
1.2.1 Stabilizing Controls......Page 20
1.2.2 Optimal Controls over Finite, Infinite, and Receding Horizons......Page 21
1.3 Models for Time-Delay Systems......Page 24
1.3.1 Input Delayed Systems......Page 25
1.3.2 State Delayed Systems......Page 28
1.4 Computation......Page 35
1.5 About the Book and Notations......Page 36
References......Page 41
2.1 Introduction......Page 43
2.2.1 General Time-Delay Systems......Page 44
2.2.2 Stability of General Time-Delay Systems......Page 45
2.3 Inequalities for Stability......Page 47
2.3.1 Matrix Inequalities......Page 48
2.3.2 Integral Inequalities for Quadratic Functions......Page 49
2.4 Stability of State Delayed Systems......Page 52
2.4.1 Lyapunov–Razumikhin Approach......Page 53
2.4.2 Lyapunov–Krasovskii Approach......Page 56
2.4.3 Discretized State Approach......Page 59
2.4.4 Extension to Systems with Time-Varying Delays......Page 61
2.5 Robust Stability of State Delayed Systems......Page 67
2.5.1 Lyapunov–Krasovskii Approach......Page 68
2.5.2 Discretized State Approach......Page 69
2.5.3 Extension to Systems with Time-Varying Delays......Page 71
2.6 Stability and Robust Stability of Distributed State Delayed Systems......Page 74
2.6.1 Lyapunov–Razumikhin Approach......Page 75
2.6.2 Lyapunov–Krasovskii Approach......Page 76
2.6.3 Lyapunov–Krasovskii Approach for Robust Stability......Page 77
References......Page 78
3.1 Introduction......Page 80
3.2.1 State Predictor Approach......Page 81
3.2.2 Reduction Transformation Approach......Page 84
3.3.1 Lyapunov–Razumikhin Approach......Page 85
3.3.2 Lyapunov–Krasovskii Approach......Page 87
3.3.3 Discretized State Approach......Page 91
3.3.4 Extension to Systems with Time-Varying Delays......Page 94
3.4 Robust Stabilizing Controls for State Delayed Systems......Page 97
3.4.1 Lyapunov–Krasovskii Approach......Page 98
3.4.2 Discretized State Approach......Page 100
3.4.3 Extension to Systems with Time-Varying Delays......Page 103
References......Page 107
4.1 Introduction......Page 109
4.2.1 Smith Predictor Approach......Page 110
4.2.2 Luenberger Observer Approach with Reduction Transformation......Page 112
4.2.3 Dynamic Feedback Control Approach with Reduction Transformation......Page 114
4.3.1 Luenberger Observer Approach......Page 116
4.3.2 Lyapunov–Razumikhin Approach......Page 118
4.3.3 Lyapunov–Krasovskii Approach......Page 121
4.3.4 Cascaded-Delay System Approach......Page 123
4.3.5 Extension to Systems with Time-Varying Delays......Page 128
4.4.1 Lyapunov–Krasovskii Approach......Page 132
4.4.2 Cascaded-Delay System Approach......Page 135
4.4.3 Extension to Systems with Time-Varying Delays......Page 141
References......Page 145
5.1 Introduction......Page 147
5.2 Guaranteed LQ Controls for Input Delayed Systems......Page 148
5.2.1 State Feedback Guaranteed LQ Control for Predictive Costs......Page 150
5.2.2 State Feedback Guaranteed LQ Control for Standard Costs......Page 152
5.2.3 Output Feedback Guaranteed LQ Control for Standard Costs......Page 155
5.3.1 State Feedback Guaranteed LQ Control......Page 160
5.3.2 Robust State Feedback Guaranteed LQ Control......Page 168
5.3.3 Output Feedback Guaranteed LQ Control......Page 171
5.4 Guaranteed mathcalHinfty Controls for Input Delayed Systems......Page 173
5.4.1 State Feedback Guaranteed mathcalHinfty Control for Predictive Costs......Page 175
5.4.2 State Feedback Guaranteed mathcalHinfty Control for Standard Costs......Page 176
5.4.3 Output Feedback Guaranteed mathcalHinfty Control for Standard Costs......Page 179
5.5 Guaranteed mathcalHinfty Controls for State Delayed Systems......Page 183
5.5.1 State Feedback Guaranteed mathcalHinfty Control......Page 184
5.5.2 Robust State Feedback Guaranteed mathcalHinfty Control......Page 192
5.5.3 Output Feedback Guaranteed mathcalHinfty Control......Page 195
References......Page 197
6.1 Introduction......Page 200
6.2.1 Fixed Horizon LQ Control for Predictive Costs......Page 201
6.2.2 Fixed Horizon LQ Control for Standard Costs......Page 204
6.3.1 Receding Horizon LQ Control for Predictive Costs......Page 218
6.3.2 Receding Horizon LQ Control for Standard Costs......Page 227
6.4 Fixed Horizon LQ Controls for State Delayed Systems......Page 236
6.4.1 Fixed Horizon LQ Control for Simple Costs......Page 237
6.4.2 Fixed Horizon LQ Control for Costs with Single Integral Terms......Page 239
6.4.3 Fixed Horizon LQ Control for Costs with Double Integral Terms......Page 243
6.5 Receding Horizon LQ Controls for State Delayed Systems......Page 249
6.5.1 Receding Horizon LQ Control for Simple Costs......Page 250
6.5.2 Receding Horizon LQ Control for Costs with Single Integral Terms......Page 252
6.5.3 Receding Horizon LQ Control for Costs with Double Integral Terms......Page 260
6.5.4 Receding Horizon LQ Control for Short Horizon Costs......Page 269
References......Page 276
7.1 Introduction......Page 278
7.2 Fixed Horizon LQG Controls for Input Delayed Systems......Page 279
7.2.1 Fixed Horizon LQG Control for Predictive Costs......Page 280
7.2.2 Fixed Horizon LQG Control for Standard Costs......Page 284
7.3.1 Receding Horizon LQG Control for Predictive Costs......Page 289
7.3.2 Receding Horizon LQG Control for Standard Costs......Page 293
7.4 Fixed Horizon LQG Controls for State Delayed Systems......Page 299
7.4.1 Fixed Horizon LQG Control for Costs with Single Integral Terms......Page 308
7.4.2 Fixed Horizon LQG Control for Costs with Double Integral Terms......Page 311
7.5 Receding Horizon LQG Controls for State Delayed Systems......Page 317
7.5.1 Receding Horizon LQG Control for Costs with Single Integral Terms......Page 319
7.5.2 Receding Horizon LQG Control for Costs with Double Integral Terms......Page 325
References......Page 331
8.1 Introduction......Page 332
8.2.1 Fixed Horizon mathcalHinfty Control for Predictive Costs......Page 333
8.2.2 Fixed Horizon mathcalHinfty Control for Standard Costs......Page 339
8.3.1 Receding Horizon mathcalHinfty Control for Predictive Costs......Page 346
8.3.2 Receding Horizon mathcalHinfty Control for Standard Costs......Page 355
8.4.1 Fixed Horizon mathcalHinfty Control for Costs with Single Integral Terms......Page 367
8.4.2 Fixed Horizon mathcalHinfty Control for Costs with Double Integral Terms......Page 371
8.5 Receding Horizon mathcalHinfty Controls for State Delayed Systems......Page 377
8.5.1 Receding Horizon mathcalHinfty Control for Costs with Single Integral Terms......Page 378
8.5.2 Receding Horizon mathcalHinfty Control for Costs with Double Integral Terms......Page 388
References......Page 399
A.1 Matrix Inertia Properties......Page 401
A.3 Inverse of Block Matrices......Page 402
A.4 Determinant......Page 403
B.1.1 Definition and Concept......Page 404
B.2.1 mathcalS-Procedure with Non-strict Inequalities......Page 405
B.2.3 Example......Page 406
B.4 Elimination of Matrix Variables......Page 407
C.1 Wirtinger-Based Integral Inequality......Page 409
C.2 Auxiliary Function-Based Integral Inequality......Page 410
D.1 Least-Squares Estimate......Page 414
D.2 Kalman Filtering......Page 417
E.1 Infinite Horizon LQ Control for Single Input Delayed Systems......Page 419
E.2 Infinite Horizon LQ Control for State Delayed Systems......Page 421
E.3 Infinite Horizon mathcalHinfty Control for State Delayed Systems......Page 423
Appendix F Program Codes......Page 426
Index......Page 427