Existence of solutions to bilinear problems with a closed-loop control
ESAIM: Control, Optimisation and Calculus of Variations, Volume 21 (2015) no. 4, pp. 989-1001.

Here we prove the existence of solutions to nonlinear differential inclusion problems with closed-loop control +A(z)=B(u,z)+f,uU(t,z),z(0)=z 0 where the operator B is bilinear with respect to the control u and the state z in reflexive, separable Banach spaces denoted Y and V, respectively. The operator A is nonlinear in V, and given a positive real number T, the set-valued map U is defined in [0,T]×V. Without making any assumptions about the convexity of U, its values are taken to be non-empty closed, decomposable subsets of Y.

Received:
DOI: 10.1051/cocv/2014055
Classification: 34A60, 35A01, 35G20, 93B52
Keywords: Nonlinear infinite system, differential inclusion, bilinear control, closed-loop control, feedback law, a priori estimates, Willett and Wong’s lemma
Clérin, Jean-Marc 1

1 Université Paris-Sorbonne (Paris IV), 10 rue Molitor, 75016 Paris, France.
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Clérin, Jean-Marc. Existence of solutions to bilinear problems with a closed-loop control. ESAIM: Control, Optimisation and Calculus of Variations, Volume 21 (2015) no. 4, pp. 989-1001. doi : 10.1051/cocv/2014055. http://www.numdam.org/articles/10.1051/cocv/2014055/

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