The MathNet Korea
Information Center for Mathematical Science

논문검색

Information Center for Mathematical Science

논문검색

Kodai Mathematical Journal
( Vol. 15 NO.2 / (1992))
Existence Theory of Optimal Controls for Distributed Parameter Systems
Jiongmin Yong,
Pages. 193-220
Abstract A unified existence theory of optimal controls for general semilinear evolutionary distributed parameter systems is established under the framework of mild (or weak) solutions for evolution equations. The theory applies to optimal control problems with the state equations being parabolic, hyperbolic partial differential equations and ordinary retarded differential equations. The approach also applies to problems governed by elliptic partial differential equations as well as variational inequalities.
Contents 1. Introduction
2. Evolution systems with compact semigroups
2.1. Statement of the control problem
2.2. Cesari property
2.3. Properties of compact semigroups
2.4. Existence of semi-admissible pairs
2.5. Existence of optimal pairs
3. Second order evolution systems
3.1. Some preliminary results on second order evolution systems
3.2. Optimal control problem, existence of optimal pairs
4. Elliptic variational inequalities
5. Appendix. Multivalued mappings
Key words distributed parameter system, existence of optimal control, Cesari property, mild solution
Mathmatical Subject Classification 49A22, 49A27