Infinite Dimensional Linear Control Systems

The book is restricted to linear equations and the most important problems (the optimal problem). As experience, results of linear equations for the treatment of the semilinear counterparts, and techniques for the time.

The main object of this book is the state of the art and it is the state of the art. frontier of research, with open problems and indications for future research.

Key features:

· Applications to optimal diffusion processes.

· Applications to optimal heat propagation processes.

· Modeling of the Newly Processed by Partial
differential equations.

· Complete bibliography.

· Includes the latest research on the subject.

· Does not assume anything from the reader except
basic functional analysis.

· Accessible to researchers and advanced graduate
students alike

· Applications to optimal diffusion processes.

· Applications to optimal heat propagation processes.

· Modeling of the Newly Processed by Partial
differential equations.

· Complete bibliography.

· Includes the latest research on the subject.

· Does not assume anything from the reader except
basic functional analysis.

· Accessible to researchers and advanced graduate
students alike

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 cost and nonuniqueness for norm optimal controls

2.7. Vanishing of the cost for time optimal controls

2.8. Singular norm optimal controls

2.9. Singular norms 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

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.