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Nicola Elia, Munther A. Dahleh, "Computational Methods for Controller Design" |
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Springer-Verlag
London Limited, 1998 |
1. Introduction (1) |
| 1.1. Background and Motivation (1) | |
| 1.2. Multi-Objective Control as Convex Optimization (2) | |
| 1.3. Solutions of Infinite Dimensional Convex Problems (2) | |
| 1.4. Main Contributions (6) | |
| 2. Mathematical Preliminaries (9) | |
| 2.1. Normed Spaces (9) | |
| 2.2. Convex Cones (12) | |
| 2.3. Convergence of Sequences (13) | |
| 2.4. Bounded Linear Operators (13) | |
| 2.5. Systems as Linear Operators on ℓn∞ (15) | |
| 2.6. Rational Matrices (17) | |
| 2.7. Notation Summary (20) | |
| 3. Multi-Objective Control (21) | |
| 3.1. Control Problem Setup (21) | |
| 3.2. Feasibility Constraints (22) | |
| 3.3. Control Objectives (26) | |
| 4. Generalized Linear Programs and Duality Theory (31) | |
| 4.1. Control Problems as Linear Programs (31) | |
| 4.2. Duality Theory Results (33) | |
| 5. ℓ1 Optimal Control with Constraints on the Step Response (39) | |
| 5.1. Problem Definition (39) | |
| 5.2. The Finite-Horizon Case (40) | |
| 5.3. ℓ1 Control with Infinite Horizon Time-domain Constraints (43) | |
| 5.4. Example (46) | |
| 6. ℓ1 - Minimization with Magnitude Constraints in the Frequency Domain (53) | |
| 6.1. Problem Statement (54) | |
| 6.2. Primal-Dual Formulation (56) | |
| 6.3. Linear Programming Approximation (59) | |
| 7. Mixed H2/ℓ1 Control (73) | |
| 7.1. Problem Statement (73) | |
| 7.2. Dual Problem (74) | |
| 7.3. Finite Dimensional Dual Approximation (78) | |
| 8. A New Computational Method for ℓ1 (89) | |
| 8.1. Introduction (89) | |
| 8.2. Notation and Problem Setup (91) | |
| 8.3. Approximation Method (93) | |
| 8.4. Convergence Properties (94) | |
| 8.5. Example (100) | |
| 9. Nonlinear Controllers for Minimizing the Worst-Case Peak to Peak Gain (105) | |
| 9.1. Notation and Preliminaries (107) | |
| 9.2. Problem Setup (108) | |
| 9.3. Finite Horizon Full State Feedback (108) | |
| 9.4. Infinite Horizon Full State Feedback (114) | |
| 9.5. Examples (118) | |
| 10. Conclusions (131) | |
| A. Proofs of Results in Chapter 5 (133) | |
| B. Proofs of Results in Chapter 6 (137) | |
| C. Proofs of Results in Chapter 8 (139) | |
| D. Proofs of Results in Chapter 9 (143) | |
| References (151) | |
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