Optimal Control: Weakly Coupled Systems and Applications

by Gajic; Zoran

• ISBN13: 9780849374296
• ISBN10: 0849374294
• Format: Hardcover
• Copyright: 2008-12-10
• Publisher: CRC Press

Summary

Since the 1960s, weakly coupled system control has become an extensive area of research. Assembling a team of leading experts in the field, Optimal Control: Weakly Coupled Systems and Applications uncovers new research and important discoveries in this burgeoning field.

Table of Contents

Preface	p. xi
Introduction	p. 1
References	p. 10
Recursive Approach for Linear Weakly Coupled Control Systems
Linear Weakly Coupled Control Systems	p. 19
Introduction	p. 19
Weakly Coupled Linear Continuous Systems	p. 19
Weakly Coupled Algebraic Lyapunov Equation	p. 21
Weakly Coupled Algebraic Riccati Equation	p. 23
Approximate Linear Regulator for Continuous Systems	p. 27
Weakly Coupled Linear Discrete Sytems	p. 28
Weakly Coupled Discrete Algebraic Lyapunov Equation	p. 28
Case Study: Discrete Catalytic Cracker	p. 30
Weakly Coupled Discrete Algebraic Riccati Equation	p. 30
Approximate Linear Regulator for Discrete Systems	p. 34
Case Study: Discrete Model of a Chemical Plant	p. 35
Output Feedback Control for Linear Weakly Coupled Systems	p. 39
Case Study: 12-Plate Absorption Column	p. 47
Notes and Comments	p. 50
References	p. 51
Quasi-Weakly Coupled Linear Control Systems	p. 55
Optimal Controller for Quasi-Weakly Coupled Linear Systems	p. 55
Cemical Reactor	p. 61
F-4 Fighter Aircraft	p. 62
Case Study: Multimachine Power System	p. 63
Reduced-Order Controller for a Class of Weakly Coupled Systems	p. 65
Numerical Example	p. 70
Case Study 1: L-1011 Fighter Aircraft	p. 71
Case Study 2: Distillation Column	p. 72
Notes	p. 74
Appendix 3.1	p. 74
References	p. 75
Weakly Coupled Singularly Perturbed Systems	p. 77
Introduction	p. 77
Weakly Coupled Singularly Perturbed Linear Control Systems	p. 78
Case Study: A Supported Beam	p. 83
Case Study: A Statellite Optimal Control Problem	p. 84
Quasi-Weakly Coupled Singularly Perturbed Control Sytems	p. 85
Case Studies	p. 91
Conclusion	p. 93
References	p. 94
Decoupling Transformation, Lyapunov Equation, and Boundary Value Problem	p. 97
Decoupling Transformation of Gajic and Shen	p. 98
Decoupling Transformation of Qureshi	p. 104
Decoupling Transformation for N Weakly Coupled Subsystems	p. 107
Decompositions of the Differential Lyapunov Equation	p. 116
Boundary Value Problem of Linear Continuous Systems	p. 117
Boundary Value Problem of Linear Discrete Systems	p. 122
References	p. 125
Stochastic Linear Weakly Coupled Systems	p. 127
Continuous Weakly Copled Stochastic Linear Control Systems	p. 128
Case Study: Electric Power System	p. 137
Discrete Weakly Coupled Stochastic Linear Control Systems	p. 139
Case Study: Distillation Column	p. 147
Stochastic Output Feedback of Discrete Systems	p. 148
Output Feedback of Quasi-Weakly Coupled Linear Discrete Systems	p. 150
Case Studies: Flight Control Systems for Aircraft	p. 158
Optimal Control of Stochastic Jump Parameter Linear Systems	p. 161
Comments	p. 169
References	p. 169
Nash Differential Games	p. 173
Weakly Coupled Linear-Quadratic Nash Games	p. 173
Solution of Coupled Algebraic Riccati Equations	p. 176
Zeroth-Order Approximation	p. 177
Solution of Higher Order of Accuracy	p. 178
Numerical Example	p. 184
	p. 186
Algorithm for Solving Coupled Algebraic Riccati Equations of Nash Differential Games	p. 186
References	p. 188
Hamiltonian Approach for Linear Weakly Coupled Control Systems
Finite Time Optimal Control via Hamiltonian Method	p. 193
Open-Loop Optimal Control in Continuous-Time	p. 193
Case Study: Distillation Column	p. 199
Open-Loop Optimal Control in Discrete-Time	p. 199
Numerical Example	p. 204
Differential Riccati Equation	p. 205
Case Study: Gas Absorber	p. 211
Difference Riccati Equation	p. 213
Numerical Example	p. 219
Concluding Remarks	p. 220
Appendix 8.1	p. 221
Appendix 8.2	p. 221
References	p. 222
Hamiltonian Method for Steady State Optimal Control and Filtering	p. 225
Exact Decomposition of the Weakly Coupled Continuous-Time Algebraic Riccati Equation	p. 225
Case Study: A Statellite Control Problem	p. 231
Optimal Filtering in Continuous-Time	p. 231
A Helicopter Filtering Problem	p. 238
Optimal Control and Filtering in Discrete-Time	p. 240
Linear-Quadratic Optimal Control	p. 241
Optimal Kalman Filtering	p. 247
Linear-Quadratic Gaussian Optimal Control Problem	p. 253
Case Study: Distillation Column	p. 256
Optimal Control of Weakly Coupled Systems with N Subsystems	p. 258
Decoupling of the Algebraic Riccati Equation	p. 258
Kalman Filtering for N Weakly Coupled Subsystems	p. 264
Linear-Quadratic Gaussian Optimal Control	p. 267
Conclusion	p. 268
Appendix 9.1	p. 269
References	p. 269
Eigenvector Method for the Hamiltonian Approach	p. 271
Introduction	p. 271
Decomposition of Weakly Coupled Algebraic Riccati Equation	p. 272
Eigenvector Method for Nonsymmetric (Nonsquare) Algebraic Riccati Equation	p. 275
Exact Decomposition Algorithm for Weakly Coupled Systems	p. 278
Examples	p. 283
Conclusion	p. 290
Justification of Step 3 of Algorithm 10.2	p. 291
On the Number of Solutions to Nonsymmetric ARE	p. 292
References	p. 292
Bilinear Weakly Coupled Control Systems
Optimal Control of Bilinear Weakly Coupled Systems	p. 297
Introduction	p. 297
Optimal Control for Weakly Coupled Bilinear Systems Using SGA	p. 299
Problem Formulation	p. 299
Design of Optimal Control Law for Weakly Coupled Bilinear Systems Using SGA	p. 302
Case Study: A Paper Making Machine	p. 307
Robust H[subscript infinity] Control for Weakly Coupled Bilinear Systems with Parameter Uncertainties Using SGA	p. 310
Problem Formulation	p. 311
Design of H[subscript infinity] Control Law for Weakly Coupled Bilinear Systems with Parameter Uncertainties Using SGA	p. 314
Case Study: A Paper Making Machine	p. 320
Conclusion	p. 321
References	p. 323
Index	p. 325
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