Maximum Principle for a Control Problem Governed by an Evolution Equation

M. Bertoldi
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M. Bertoldi: University of Trento

Journal of Optimization Theory and Applications, 2000, vol. 105, issue 2, No 1, 263-276

Abstract: Abstract We prove the maximum principle for an optimal control problem governed by the system $$y'(t) + A(t)y(t) = f(t,y(t),u(t)),{\text{ }}u(t) \in U(t), $$ with state constraint $$(y(0),y(T)) \in C \subset H \times H $$ , under three different hypotheses: (H1) C is a convex set with nonempty interior; (H2) $$C = \{ y_0 \} \times C_{0,} {\text{ with }}C_0 $$ a convex set with nonempty interior in H and the evolution system satisfying compactness hypotheses; (H3) the periodic case $$y(0) = y(T)$$ , with the evolution system satisfying compactness hypotheses. We do not assume the controls to be bounded. We give some examples for distributed control problems.

Keywords: optimal control; distributed-parameter systems; Pontryagin maximum principle; Ekeland variational principle; unbounded controls (search for similar items in EconPapers)
Date: 2000
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DOI: 10.1023/A:1004654800011

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