Optimal control : weakly coupled systems and applications

Unique in scope, Optimal Control: Weakly Coupled Systems and Applications provides complete coverage of modern linear, bilinear, and nonlinear optimal control algorithms for both continuous-time and discrete-time weakly coupled systems, using deterministic as well as stochastic formulations. This book presents numerous applications to real world systems from various industries, including aerospace, and discusses the design of subsystem-level optimal filters. Organized into independent chapters for easy access to the material, this text also contains several case studies, examples, exercises, computer assignments, and formulations of research problems to help instructors and students.

Preface	p. xi
Chapter 1 Introduction	p. 1
References	p. 10
Part I Recursive Approach for Linear Weakly Coupled Control Systems
Chapter 2 Linear Weakly Coupled Control Systems	p. 19
2.1 Introduction	p. 19
2.2 Weakly Coupled Linear Continuous Systems	p. 19
2.2.1 Weakly Coupled Algebraic Lyapunov Equation	p. 21
2.2.2 Weakly Coupled Algebraic Riccati Equation	p. 23
2.3 Approximate Linear Regulator for Continuous Systems	p. 27
2.4 Weakly Coupled Linear Discrete Sytems	p. 28
2.4.1 Weakly Coupled Discrete Algebraic Lyapunov Equation	p. 28
2.4.2 Case Study: Discrete Catalytic Cracker	p. 30
2.4.3 Weakly Coupled Discrete Algebraic Riccati Equation	p. 30
2.5 Approximate Linear Regulator for Discrete Systems	p. 34
2.5.1 Case Study: Discrete Model of a Chemical Plant	p. 35
2.6 Output Feedback Control for Linear Weakly Coupled Systems	p. 39
2.6.1 Case Study: 12-Plate Absorption Column	p. 47
2.7 Notes and Comments	p. 50
References	p. 51
Chapter 3 Quasi-Weakly Coupled Linear Control Systems	p. 55
3.1 Optimal Controller for Quasi-Weakly Coupled Linear Systems	p. 55
3.1.1 Cemical Reactor	p. 61
3.1.2 F-4 Fighter Aircraft	p. 62
3.1.3 Case Study: Multimachine Power System	p. 63
3.2 Reduced-Order Controller for a Class of Weakly Coupled Systems	p. 65
3.2.1 Numerical Example	p. 70
3.2.2 Case Study 1: L-1011 Fighter Aircraft	p. 71
3.2.3 Case Study 2: Distillation Column	p. 72
3.3 Notes	p. 74
Appendix 3.1	p. 74
References	p. 75
Chapter 4 Weakly Coupled Singularly Perturbed Systems	p. 77
4.1 Introduction	p. 77
4.2 Weakly Coupled Singularly Perturbed Linear Control Systems	p. 78
4.2.1 Case Study: A Supported Beam	p. 83
4.2.2 Case Study: A Statellite Optimal Control Problem	p. 84
4.3 Quasi-Weakly Coupled Singularly Perturbed Control Sytems	p. 85
4.3.1 Case Studies	p. 91
4.4 Conclusion	p. 93
References	p. 94
Chapter 5 Decoupling Transformation, Lyapunov Equation, and Boundary Value Problem	p. 97
5.1 Decoupling Transformation of Gajic and Shen	p. 98
5.1.1 Decoupling Transformation of Qureshi	p. 104
5.2 Decoupling Transformation for N Weakly Coupled Subsystems	p. 107
5.3 Decompositions of the Differential Lyapunov Equation	p. 116
5.4 Boundary Value Problem of Linear Continuous Systems	p. 117
5.5 Boundary Value Problem of Linear Discrete Systems	p. 122
References	p. 125
Chapter 6 Stochastic Linear Weakly Coupled Systems	p. 127
6.1 Continuous Weakly Copled Stochastic Linear Control Systems	p. 128
6.1.1 Case Study: Electric Power System	p. 137
6.2 Discrete Weakly Coupled Stochastic Linear Control Systems	p. 139
6.2.1 Case Study: Distillation Column	p. 147
6.3 Stochastic Output Feedback of Discrete Systems	p. 148
6.3.1 Output Feedback of Quasi-Weakly Coupled Linear Discrete Systems	p. 150
6.3.2 Case Studies: Flight Control Systems for Aircraft	p. 158
6.4 Optimal Control of Stochastic Jump Parameter Linear Systems	p. 161
6.5 Comments	p. 169
References	p. 169
Chapter 7 Nash Differential Games	p. 173
7.1 Weakly Coupled Linear-Quadratic Nash Games	p. 173
7.2 Solution of Coupled Algebraic Riccati Equations	p. 176
7.2.1 Zeroth-Order Approximation	p. 177
7.2.2 Solution of Higher Order of Accuracy	p. 178
7.3 Numerical Example	p. 184
Appendix 7.1 p. 186
Appendix 7.2 Algorithm for Solving Coupled Algebraic Riccati Equations of Nash Differential Games	p. 186
References	p. 188
Part II Hamiltonian Approach for Linear Weakly Coupled Control Systems
Chapter 8 Finite Time Optimal Control via Hamiltonian Method	p. 193
8.1 Open-Loop Optimal Control in Continuous-Time	p. 193
8.1.1 Case Study: Distillation Column	p. 199
8.2 Open-Loop Optimal Control in Discrete-Time	p. 199
8.2.1 Numerical Example	p. 204
8.3 Differential Riccati Equation	p. 205
8.3.1 Case Study: Gas Absorber	p. 211
8.4 Difference Riccati Equation	p. 213
8.4.1 Numerical Example	p. 219
8.5 Concluding Remarks	p. 220
Appendix 8.1	p. 221
Appendix 8.2	p. 221
References	p. 222
Chapter 9 Hamiltonian Method for Steady State Optimal Control and Filtering	p. 225
9.1 Exact Decomposition of the Weakly Coupled Continuous-Time Algebraic Riccati Equation	p. 225
9.1.1 Case Study: A Statellite Control Problem	p. 231
9.2 Optimal Filtering in Continuous-Time	p. 231
9.2.1 A Helicopter Filtering Problem	p. 238
9.3 Optimal Control and Filtering in Discrete-Time	p. 240
9.3.1 Linear-Quadratic Optimal Control	p. 241
9.3.2 Optimal Kalman Filtering	p. 247
9.3.3 Linear-Quadratic Gaussian Optimal Control Problem	p. 253
9.3.4 Case Study: Distillation Column	p. 256
9.4 Optimal Control of Weakly Coupled Systems with N Subsystems	p. 258
9.4.1 Decoupling of the Algebraic Riccati Equation	p. 258
9.4.2 Kalman Filtering for N Weakly Coupled Subsystems	p. 264
9.4.3 Linear-Quadratic Gaussian Optimal Control	p. 267
9.5 Conclusion	p. 268
Appendix 9.1	p. 269
References	p. 269
Chapter 10 Eigenvector Method for the Hamiltonian Approach	p. 271
10.1 Introduction	p. 271
10.2 Decomposition of Weakly Coupled Algebraic Riccati Equation	p. 272
10.3 Eigenvector Method for Nonsymmetric (Nonsquare) Algebraic Riccati Equation	p. 275
10.4 Exact Decomposition Algorithm for Weakly Coupled Systems	p. 278
10.5 Examples	p. 283
10.6 Conclusion	p. 290
Appendix 10.1 Justification of Step 3 of Algorithm 10.2	p. 291
Appendix 10.2 On the Number of Solutions to Nonsymmetric ARE	p. 292
References	p. 292
Part III Bilinear Weakly Coupled Control Systems
Chapter 11 Optimal Control of Bilinear Weakly Coupled Systems	p. 297
11.1 Introduction	p. 297
11.2 Optimal Control for Weakly Coupled Bilinear Systems Using SGA	p. 299
11.2.1 Problem Formulation	p. 299
11.2.2 Design of Optimal Control Law for Weakly Coupled Bilinear Systems Using SGA	p. 302
11.2.3 Case Study: A Paper Making Machine	p. 307
11.3 Robust H[subscript infinity] Control for Weakly Coupled Bilinear Systems with Parameter Uncertainties Using SGA	p. 310
11.3.1 Problem Formulation	p. 311
11.3.2 Design of H[subscript infinity] Control Law for Weakly Coupled Bilinear Systems with Parameter Uncertainties Using SGA	p. 314
11.3.3 Case Study: A Paper Making Machine	p. 320
11.4 Conclusion	p. 321
References	p. 323
Index	p. 325

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