Annali di Matematica Pura ed Applicata

, Volume 154, Issue 1, pp 259–279 | Cite as

On the optimal control and relaxation of nonlinear infinite dimensional systems

  • Nikolaos S. Papageorgiou
Article

Summary

In this paper we study optimal control problems for infinite dimensional systems governed by a semilinear evolution equation. First under appropriate convexity and growth conditions, we establish the existence of optimal pairs. Then we drop the convexity hypothesis and we pass to a larger system known as the « relaxed system ». We show that this system has a solution and the value of the relaxed optimization problem is equal to the value of the original one. Next we restrict our attention to linear systems and establish two « bang-bang » type theorems. Finally we present some examples from systems governed by partial differential equations.

Keywords

Differential Equation Growth Condition Linear System Partial Differential Equation Control Problem 

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Copyright information

© Fondazione Annali di Matematica Pura ed Applicata 1989

Authors and Affiliations

  • Nikolaos S. Papageorgiou
    • 1
  1. 1.1015 Department of MathematicsUniversity of CaliforniaDavisUSA

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