Abstract
The aim of this paper is to investigate a regional constrained optimal control problem for a class of semilinear distributed systems, which are linear in the control but nonlinear in the state. For a quadratic cost functional and a closed convex set of admissible controls, the existence of an optimal control is proven, and then this is characterized for three cases of constraints. A useful algorithm is developed, and the approach is illustrated through simulations for a heat equation.
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