Infinite Dimensional Linear Control Systems - The Time Optimal and Norm Optimal Problems

Abstract

PREFACE CHAPTER 1: INTRODUCTIONP> 1.1 Finite dimensional systems: the maximum principle. 1.2. Finite dimensional systems: existence and uniqueness. 1.3. Infinite dimensional systems. CHAPTER 2: SYSTEMS WITH STRONGLY MEASURABLE CONTROLS, I 2.1. The reachable space and the bang-bang property 2.2. Reversible systems 2.3. The reachable space and its dual, I 2.4. The reachable space and its dual, II 2.5. The maximum principle 2.6. Vanishing of the costate and nonuniqueness for norm optimal controls 2.7. Vanishing of the costate for time optimal controls 2.8. Singular norm optimal controls 2.9. Singular norm optimal controls and singular functionals CHAPTER 3: SYSTEMS WITH STRONGLY MEASURABLE CONTROLS, II 3.1. Existence and uniqueness of optimal controls 3.2. The weak maximum principle and the time optimal problem 3.3. Modeling of parabolic equations 3.4. Weakly singular extremals 3.5. More on the weak maximum principle 3.6. Convergence of minimizing sequences and stability of optimal controls CHAPTER 4: OPTIMAL CONTROL OF HEAT PROPAGATION 4.1. Modeling of parabolic equations 4.2. Adjoints 4.3. Adjoint semigroups 4.4. The reachable space 4.5. The reachable space and its dual, I 4.6. The reachable space and its dual, II 4.7. The maximum principle 4.8. Existence, uniqueness and stability of optimal controls 4.9. Examples and applications CHAPTER 5: OPTIMAL CONTROL OF DIFFUSIONS 5.1. Modeling of parabolic equations 5.2. Dual spaces 5.3. The reachable space and its dual 5.4. The maximum principle 5.5. Existence of optimal controls uniqueness and stability of supports 5.6. Examples and applications. CHAPTER 6: APPENDIX 6.1 Self adjoint operators, I 6.2 Self adjoint operators, II 6.3 Related research REFERENCES NOTATION AND SUBJECT INDEX.