On some optimal control problems governed by a state equation with memory
ESAIM: Control, Optimisation and Calculus of Variations, Volume 14 (2008) no. 4, pp. 725-743.

The aim of this paper is to study problems of the form: inf (uV) J(u) with J(u):= 0 1 L(s,y u (s),u(s))ds+g(y u (1)) where V is a set of admissible controls and y u is the solution of the Cauchy problem: x ˙(t)=f(.,x(.)),ν t +u(t),t(0,1), x(0)=x 0 and each ν t is a nonnegative measure with support in [0,t]. After studying the Cauchy problem, we establish existence of minimizers, optimality conditions (in particular in the form of a nonlocal version of the Pontryagin principle) and prove some regularity results. We also consider the more general case where the control also enters the dynamics in a nonlocal way.

DOI: 10.1051/cocv:2008005
Classification: 34K35, 49K25
Keywords: optimal control, memory
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Carlier, Guillaume; Tahraoui, Rabah. On some optimal control problems governed by a state equation with memory. ESAIM: Control, Optimisation and Calculus of Variations, Volume 14 (2008) no. 4, pp. 725-743. doi : 10.1051/cocv:2008005. http://archive.numdam.org/articles/10.1051/cocv:2008005/

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