Chapter I. Minimization of Functions and Unilateral Boundary Value Problems
1. Minimization of Coercive Forms
2. A Direct Solution of Certain Variational Inequalities
3. Examples
4. A Comparison Theorem
5. Non Coercive Forms
Notes
Chapter II. Control of Systems Governed by Elliptic Partial Differential Equations
1. Control of Elliptic Variational Problems
2. First Applications
3. A Family of Examples with N = 0 and U_ad Arbitrary
4. Observation on the Boundary
5. Control and Observation on the Boundary. Case of the Dirichlet Problem
6. Constraints on the State
7. Existence Results for Optimal Controls
8. First Order Necessary Conditions
Notes
Chapter III. Control of Systems Governed by Parabolic Partial Differential Equations
1. Equations of Evolution
2. Problems of Control
3. Examples
4. Decoupling and Integro-Differential Equation of Riccati Type (I)
5. Decoupling and Integro-Differential Equation of Riccati Type (II)
6. Behaviour as T -> + infty
7. Problems which are not Necessarily Coercive.
8. Other Observations of the State and other Types of Control
9. Boundary Control and Observation on the Boundary or of the Final State for a System Governed by a Mixed Dirichlet Problem
10. Controllability
11. Control via Initial Conditions; Estimation
12. Duality
13. Constraints on the Control and the State
14. Non Quadratic Cost Functions
15. Existence Results for Optimal Controls
16. First Order Necessary Conditions
17. Time Optimal Control
18. Miscellaneous
Notes
Chapter IV. Control of Systems Governed by Hyperbolic Equations or by Equations which are well posed in the petrowsky Sense
1. Second order Evolution Equations
2. Control Problems
3. Transposition and Applications to Control
4. Examples
5. Decoupling
6. Control via Initial Conditions. Estimation
7. Boundary Control (I)
8. Boundary Control (II)
9. Parabolic-Hyperbolic Systems
10. Existence Theorems
Notes
Chapter V. Regularization, Approximation and Penalization
1. Regularization
2. Approximation in Terms of Systems of Cauchy-KoWaleska Type
3. Penalization
Notes
Bibliography
Subject Index