Adam Kowalewski (AGH University of Science and Technology, Kraków, Poland)

Optimal control of parabolic systems with delays
Friday 24 November 2017 at 14.00, JCMB 5326

Abstract

We consider an optimal boundary control problem for a linear parabolic system in which time delays appear in the integral form with k ∈ (0,c) in the state equation and with h ∈ (0,b) in the Neumann boundary condition.

Sufficient conditions for the existence of a unique solution for such parabolic system are presented. The performance functionals have quadratic form. The time horizon T is fixed. Finally, we impose some constraints on the boundary control. Making use of Lion's framework necessary and sufficient conditions of optimality are derived for a linear quadratic problem.

A simple example of application is also provided.

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