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 ^o 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.