Buch, Englisch, 272 Seiten
Challenges, Progress and Applications
Buch, Englisch, 272 Seiten
ISBN: 978-1-394-46182-0
Verlag: John Wiley & Sons Inc
Solve irregular, infinite-dimensional, and asymmetric LQ control problems
Standard LQ control theory breaks down when regularity assumptions fail, state dimensions become infinite, or controllers have asymmetric information or roles. Nonstandard Linear Quadratic Optimal Control identifies the root causes of these breakdowns and introduces decoupling-based methods for forward-backward difference/differential equations to resolve them across both discrete-time and continuous-time settings.
The book develops FBDEs decoupling techniques that enable optimal feedback controller design and feedback stabilization. Coverage extends to irregular LQ control of deterministic and stochastic systems with additive and multiplicative noise, stochastic LQ control with input delay and state delay, infinite-dimensional LQ control of partial differential systems, decentralized LQ control with various asymmetric information structures, open-loop and closed-loop Stackelberg game LQ control, and applications in networked control and multi-agent systems. Each topic connects theoretical results directly to engineering applications including autonomous driving.
Readers will also find: - A proposed general method of decoupling FBDEs to address the difficulties encountered in analytical design
- Controller and stabilization conditions for different non-standard LQ control characterized by distinct self-developed Riccati-like equations
Designed for professionals and researchers in control theory, systems engineering, and autonomous driving, this book serves as both a theoretical reference and a practical toolkit. Graduate students with grounding in algebra, probability, and classical LQ regulation will find the structured progression from fundamentals to advanced applications accessible.
Autoren/Hrsg.
Weitere Infos & Material
List of Figures xvii
List of Tables xix
Foreword xxi
Preface xxvii
Acknowledgments xxix
Acronyms xxxi
List of Symbols xxxiii
Introduction xxxv
PART I IRREGULAR LQ CONTROL
1 Irregular LQ Optimal Control 3
1.1 Problem Formulation 3
1.2 Finite Horizon Case 4
1.2.1 Solution via the Maximum Principle Method 4
1.2.2 Solution via the Complete Square Method 8
1.3 Infinite Horizon Case 12
1.3.1 Regular Case 13
1.3.2 Irregular Case 14
1.4 Notes and Comments 17
2 Stochastic Irregular LQ Optimal Control with Additive Noise 19
2.1 Problem Formulation 19
2.2 Preliminaries 21
2.2.1 Maximum Principle 21
2.2.2 Regular Case 22
2.3 Solution to Problem 24
2.4 Notes and Comments 27
3 Stochastic Irregular LQ Control with Multiplicative Noise 29
3.1 Problem Formulation 29
3.1.1 Preliminaries 30
3.1.2 Solution to Problem 35
3.2 Numerical Examples 38
3.3 Notes and Comments 38
PART II LQ CONTROL OF INFINITEDIMENSION SYSTEMS: TIMEDELAY SYSTEMS
4 LQ Control for Stochastic Systems with a Single Input Delay 43
4.1 DiscreteTime Case 43
4.1.1 Problem Formulation 43
4.1.2 Finite Horizon Stochastic LQ control 45
4.1.3 Infinite Horizon Stochastic LQ control 50
4.1.4 Numerical Examples 63
4.2 ContinuousTime Case 64
4.2.1 Problem Formulation 64
4.2.2 Finite Horizon Stochastic LQ Control 65
4.2.3 Infinite Horizon Stochastic LQ Control 74
4.2.4 Numerical Examples 86
4.3 Notes and Comments 87
5 LQ Control for Stochastic Systems with Multiple Input Delays 91
5.1 Discretetime Case 91
5.1.1 Problem Formulation 91
5.1.2 Transform Delayed Systems into DelayFree Ones 93
5.1.3 Stabilization of the Stochastic System with Multiple Input Delays 101
5.2 Continuoustime Case 111
5.2.1 Finite Horizon Stochastic LQ Control 111
5.2.2 Infinite Horizon Stochastic LQ Control 117
5.3 Notes and Comments 120
6 LQ Control Problem for It ˆo Systems with State Delays 121
6.1 Problem Formulation 121
6.2 Solution to Problem 122
6.3 Notes and Comments 124
7 Other DelayRelated Stochastic LQ Control 125
7.1 Stochastic LQ Control for Delayed MeanField Systems: Discrete Time 125
7.1.1 Finite Horizon Optimal Control 126
7.1.2 Infinite Horizon Optimal Control 128
7.2 Stochastic LQ Control for Delayed Meanfield Systems: Continuous Time 129
7.2.1 Finite Horizon Optimal Control 129
7.2.2 Infinite Horizon Optimal Control 131
7.3 Stochastic LQ Control for Delayed Markov Systems 133
7.3.1 Finite Horizon Optimal Control 134
7.3.2 Infinite Horizon Optimal Control 136
7.4 Stochastic LQ Control for Delayed Markov Systems with Multiplicative Noises 138
7.4.1 Finite Horizon Optimal Control 139
7.4.2 Infinite Horizon Optimal Control 145
7.5 Notes and Comments 148
PART III LQ CONTROL FOR INFINITEDIMENSION SYSTEMS: PARTIAL DIFFERENTIAL SYSTEM
8 LQ Control for FirstOrder Hyperbolic Systems 151
8.1 Problem Formulation 151
8.2 Main Results 152
8.3 A Continuous Method to Verify the Main Results 155
8.4 Numerical Examples 157
8.5 Notes and Comments 158
9 LQ Control for SecondOrder Parabolic Systems 159
9.1 Problem Formulation 159
9.2 Main Results 160
9.2.1 Discretization Problem 160
9.2.2 Optimal Controller Design for Discretization Problem 161
9.2.3 Optimal Controller Design for the Original Problem 163
9.3 Numerical Examples 164
9.4 Notes and Comments 166
PART IV LQ CONTROL WITH ASYMMETRIC INFORMATION
10 Decentralized LQ Control with Information Inclusion Structure 169
10.1 Problem Formulation 169
10.2 Optimal Control Design 171
10.3 Solving the Coupled Forward and Backward Riccati Equations 176
10.4 Numerical Examples 178
10.5 Notes and Comments 182
11 Decentralized LQG Control with dStep Delayed Information Sharing Pattern 183
11.1 Problem Formulation 183
11.2 Optimal Estimation 186
11.3 Optimal Control Design 189
11.4 Asymptotically Optimal Solution by Decoupling the Control Gain and Estimation Gain 193
11.5 Numerical Examples 194
11.6 Notes and Comments 196
12 Decentralized LQ Control with Private Input and Measurement Information 197
12.1 Problem Formulation 197
12.2 Preliminaries 198
12.3 Decentralized Control with Input Sharing Pattern 199
12.4 Decentralized Control with Private Input Information 200
12.5 Extension to the Case with Multiple Inputs and Application to MultiAgent Systems 203
12.6 Numerical Examples 206
12.7 Notes and Comments 207
PART V LQ CONTROL WITH ASYMMETRIC POSITION
13 OpenLoop Stackelberg Strategy 211
13.1 Problem Formulation 211
13.2 Main Results 212
13.2.1 Optimization for the Follower 212
13.2.2 Optimization for the Leader 214
13.2.3 Solution to Problem 219
13.2.4 Numerical Examples 222
13.3 Notes and Comments 222
14 OpenLoop Stackelberg Strategy with Time Delay 223
14.1 Difference Game 223
14.1.1 Problem Formulation 223
14.1.2 Optimization for the Follower 224
14.1.3 Optimization for the Leader 226
14.1.4 Solution to Problem 227
14.2 Differential Game 234
14.2.1 Problem Formulation 234
14.2.2 Optimization for the Follower 235
14.2.3 Optimization for the Leader 236
14.2.4 Solution to Problem 237
14.3 Notes and Comments 243
15 Linear ClosedLoop Stackelberg Strategy 245
15.1 Problem Formulation 245
15.2 Main Result 246
15.2.1 Optimization for the Follower 248
15.2.2 Optimization for the Leader 252
15.2.3 Solution to Problem 256
15.3 Numerical Examples 258
15.4 Notes and Comments 259
PART VI APPLICATIONS IN NETWORKED CONTROL SYSTEMS
16 Stabilization Control for NCSs 263
16.1 Problem Formulation 263
16.2 Main Results 265
16.2.1 Optimal LQ Control and Stabilization of Networked Control System 265
16.2.2 Existence Theorem of the Maximum Packet Dropout Rate 267
16.2.3 Maximum Packet Dropout Rate and Maximum Allowable Delay Bound 269
16.3 Notes and Comments 272
17 LQ Control with Remote and Local Controllers 273
17.1 Finite Horizon Optimal Control 273
17.1.1 Problem Formulation 273
17.1.2 Solution to Problem 274
17.2 Infinite Horizon Optimal Control 279
17.2.1 Problem Formulation 279
17.2.2 Solution to Problem 280
17.3 Numerical Examples 285
17.3.1 Finite Horizon Case 286
17.3.2 Infinite Horizon Case 287
17.4 Notes and Comments 288
18 Optimal Consensus of MultiAgent Systems 291
18.1 Problem Formulation and Preliminaries 291
18.1.1 Problem Formulation 292
18.1.2 Preliminaries 292
18.2 Distributed Optimal Controller Design 294
18.2.1 Consensus of MultiAgent System Based on Relative Error Feedback 294
18.2.2 Comparison with Traditional Consensus Algorithms 299
18.2.3 Special Case: Consensus of MultiAgent Systems via State Feedback Controller 299
18.3 Numerical Simulations 302
18.4 Notes and Comments 305
19 Asymptotically Optimal Distributed Consensus of Heterogeneous MultiAgent Systems 307
19.1 Problem Formulation 307
19.2 Main Results 308
19.2.1 State Consensus of Heterogeneous MultiAgent Systems 308
19.2.2 Comparison with Traditional Consensus Algorithms 314
19.2.3 Output Consensus of Heterogeneous MultiAgent Systems 315
19.3 Numerical Simulations 318
19.4 Notes and Comments 319
A Classical LQR for Deterministic Systems 323
B Classical LQR for Stochastic Systems 325
C Solution to Linear DiscreteTime FBSDEs 327
C.1 Problem Formulation 327
C.2 The Explicit Solution to FBSDEs 329
C.2.1 Solvability of FBSDEs 331
C.2.2 Unique Solvability of FBSDEs 332
D Solution to Linear DiscreteTime FBSDEs with Time Delay 335
D.1 Problem Formulation 335
D.2 The Explicit Solution to FBSDEs 336
E Solution to Linear ContinuousTime FBSDEs with Time Delay 343
E.1 Problem Formulation 343
E.2 The Method of Discretization 344
E.3 The Explicit Solution to FBSDEs 348
F Solution to Linear ContinuousTime FBSDEs with State Delay 355
F.1 Problem Formulation 356
F.2 The Explicit Solution to FBSDEs 356
F.2.1 Corresponding Discretetime FBSDEs 357
F.2.2 Limitation of the Discretetime FBSDEs 361
F.2.3 Proof of Theorem F.1 365
Index
