Parallel Algorithms for Optimal Control of Large Scale Linear Systems

One - Theoretical Concepts.- 2. Linear-Quadratic Control Problems.- 2.1 Introduction.- 2.2 Recursive Methods for Singularly Perturbed Linear Continuous Systems.- 2.2.1 Parallel Algorithm for Solving Algebraic Lyapunov Equation.- 2.2.2 Parallel Algorithm for Solving Algebraic Riccati Equation.- 2.2.3 Case Study: Magnetic Tape Control Problem.- 2.3 Recursive Methods for Weakly Coupled Linear Continuous Systems.- 2.3.1 Parallel Algorithm for Solving Algebraic LyapIIDov Equation.- 2.3.2 Parallel Algorithm for Solving Algebraic Riccati Equation.- 2.4 Approximate Linear Regulator Problem for Continuous Systems.- 2.5 Recursive Methods for Singularly Perturbed Linear Discrete Systems.- 2.5.1 Parallel Algorithm for Solving Algebraic Lyapunov Equation.- 2.5.2 Case Study: An F-8 Aircraft.- 2.5.3 Parallel Algorithm for Solving Algebraic Riccati Equation.- 2.6 Approximate Linear Regulator for Discrete Systems.- 2.6.1 Case Study: Discrete Model of An F-8 Aircraft.- 2.7 Recursive Methods for Weakly Coupled Linear Discrete Systems.- 2.7.1 Parallel Algorithm for Solving Discrete Algebraic Lyapunov Equation.- 2.7.2 Case Study: Discrete Catalytic Cracker.- 2.7.3 Parallel Algorithm for Solving Algebraic Riccati Equation.- 2.7.4 Case Study: Discrete Model of a Chemical Plant.- 2.8 Notes and Comments.- 3. Decoupling Transformations.- 3.1 Introduction.- 3.2 Decoupling Transformation for Singularly Perturbed Linear Systems.- 3.3 Decoupling Transformation for Weakly Coupled Linear Systems.- 3.4 New Versions of Decoupling Transformations.- 3.4.1 New Decoupling Transformation for Linear Weakly Coupled System.- 3.4.2 New Decoupling Transformation for Linear Singularly Perturned Systems.- 3.5 Decomposition of the Differential Lyapunov Equations.- 3.6 Boundary Value Problem for Linear Continuous Weakly Coupled System.- 3.7 Boundary Value Problem for Linear Discrete-Time Weakly Coupled System.- 4. Output feedback control.- 4.1. Introduction.- 4.2 Output Feedback for Singularly Perturbed Linear Systems.- 4.3 Case Study: Fluid Catalytic Cracker.- 4.4 Output Feedback for Linear Weakly Coupled Systems.- 4.5 Case Study: Twelve Plate Absorption Column.- 5. Linear Stochastic Systems.- 5.1 Recursive Approach to Singularly Perturbed Linear Stochastic Systems.- 5.2 Case Study: F-S Aircraft LQG Controller.- 5.3 Recursive Approach to Weakly Coupled Linear Stochastic system.- 5.4 Case Study: Electric Power System.- 5.5 Parallel Reduced-Order Controllers for Stochastic Linear Discrete Singularly Perturbed Systems.- 5.6 Case Study: Discrete Steam Power System.- 5.7 Linear-Quadratic Gaussian Control of Discrete Weakly Coupled Systems at Steady State.- 5.8 Case Study: Distillation Column.- Appendix 5.1.- 6. Open-Loop Optimal Control Problems.- 6.1 Open-Loop Singularly Perturbed Control Problem.- 6.2 Case Study: Magnetic Tape Control.- 6.3 Open-Loop Weakly Coupled Optimal Control Problem.- 6.4 Case Study: Distillation Column.- 6.5 Open-Loop Discrete Singularly Perturbed Control Problem.- 6.6 Case Study: F-8 Aircraft Control Problem.- 6.7 Open-Loop Discrete Weakly Coupled Control Problem.- 6.8 Numerical Example.- 6.9 Conclusion.- Appendix 6.1.- Appendix 6.2.- Appendix 6.3.- Appendix 6.4.- 7. Exact Decompositions of Algebraic Riccati Equations.- 7.1 The Exact Decomposition of the Singularly Perturbed Algebraic Riccati Equation.- 7.2 Numerical Example.- 7.3 The Exact Decomposition of the Weakly Coupled Algebraic Riccati Equation.- 7.4 Case Study: A Satellite Control Problem.- 7.5 Conclusion.- Appendix 7.1.- Appendix 7.2.- Appendix 7.3.- 8. Differential and Difference Riccati Equations.- 8.1 Recursive Solution of the Singularly Perturbed Differential Riccati Equation.- 8.2 Case Study: A Synchronous Machine Connected to an Infinite Bus.- 8.3 Recursive Solution of the Riccati Differential Equation of Weakly Coupled Systems.- 8.4 Case Study: Gas Absorber.- 8.5 Reduced-Order Solution of the Singularly Perturbed Matrix Difference Riccati Equation.- 8.6 Case Study: Linearized Discrete Model of an F-8 Aircraft.- 8.7 Reduced-Order Solution of the Weakly Coupled Matrix Difference Riccati Equation.- 8.8 Numerical Example.- Appendix 8.1.- Appendix 8.2.- Appendix 8.3.- Appendix 8.4.- Two - Applications.- 9. Quasi Singularly Perturbed and Weakly Coupled Linear Systems.- 9.1 Linear Control of Quasi Singularly Perturbed Hydro Power Plants.- 9.2 Case Study: Hydro Power Plant.- 9.2.1 Weakly Controlled Fast Modes Structure.- 9.2.2 Strongly Controlled Slow Modes Structure.- 9.2.3 Weakly Controlled Fast Modes and Strongly Controlled Slow Modes Structure.- 9.3 Reduced-Order Design of Optimal Controller for Quasi Weakly Coupled Linear System.- 9.4 Case Studies.- 9.4.1 Chemical Reactor.- 9.4.2 F-4 Fighter Aircraft.- 9.4.3 Multimachine Power System.- 9.5 Reduced-Order Solution for a Class of Linear-Quadratic Optimal Control Problems.- 9.5.1 Numerical Example.- 9.6 Case Studies.- 9.6.1 Case Study 1: L-1011 Fighter Aircraft.- 9.6.2 Case Study 2: Distillation Column.- Notes.- Appendix 9.1.- 10. Singularly Perturbed Weakly Coupled Linear Control Systems.- 10.1 Introduction.- 10.2 Singularly Perturbed Weakly Coupled Linear Control Systems.- 10.3 Case Studies.- 10.3.1 Case Study 1: A Model of Supported Beam.- 10.3.2 Case Study 2: A Satellite Control Problem.- 10.4 Quasi Singularly Perturbed Weakly Coupled Linear Control Systems.- 10.5 Case Studies.- 10.6 Conclusion.- Appendix 10.1.- 11. Stochastic Output Feedback of Linear Discrete Systems.- 11.1 Introduction.- 11.2 Output Feedback of Quasi Weakly Coupled Linear Stochastic Discrete Systems.- 11.3 Case Study: Flight Control System for Aircrafts.- 11.4 Output Feedback of Singularly Perturbed Stochastic Discrete Systems.- 11.4.1 Problem Formulation.- 11.4.2 Slow-Fast Lower Order Decomposition.- 1111.5 Case Study: Discrete Model of a Steam Power System.- 12. Applications to Differential Games.- 12.1 Weakly Coupled Linear-Quadratic Nash Games.- 12.2 Solution of Coupled Algebraic Riccati Equations.- 12.2.1 Zeroth-Order Approximation.- 12.2.2 Solution of Higher Order of Accuracy.- 12.3 Numerical Examples.- Appendix 12.1.- Appendix 12.2.- 13. Recursive Approach to High Gain and Cheap Control Problems.- 13.1 Linear-Quadratic Cheap and High Gain Control Problems.- 13.1.1 High Gain Feedback Control.- 13.1.2 Cheap Control Problem.- 13.1.3 Parallel Algorithm for Solving Algebraic Riccati Equations for Cheap Control and High Gain Feedback.- 13.2 Case Study: Large Space Structure.- 13.3 Decomposition of the Open-Loop Cheap Control Problem.- 13.4 Numerical Example.- 13.5 Exact Decomposition of the Algebraic Riccati Equation for Cheap Control Problem.- 13.6 Numerical Example.- Appendix 13.1.- 14. Linear Approach to Bilinear Control Systems.- 14.1 Introduction.- 14.2 Reduced-Order Open Loop Optimal Control of Bilinear Systems.- 14.3 Reduced-Order Closed Loop Optimal Control of Bilinear Systems.- 14.3.1 Composite Near-Optimal Control of Bilinear Systems.- 14.4 Case Study: Induction Motor Drives.- 14.5 Near-Optimal Control of Singularly Perturbed Bilinear Systems.- 14.6 Optimal Control of Weakly Coupled Bilinear Systems.- 14.6.1 Open-Loop Control of Weakly Coupled Bilinear Systems.- 14.6.2 Closed-Loop Control of Weakly Coupled Bilinear Systems.- 14.7 Case Study: A Paper Making Machine.- 14.8 Conclusion.