Existence of solutions to bilinear problems with a closed-loop control
Université Paris-Sorbonne (Paris
IV), 10 rue
Revised: 17 September 2014
Here we prove the existence of solutions to nonlinear differential inclusion problems with closed-loop control ż + A(z) = B(u,z) + f,u ∈ U(t,z),z(0) = z0 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.
Mathematics Subject Classification: 34A60 / 35A01 / 35G20 / 93B52
Key words: Nonlinear infinite system / differential inclusion / bilinear control / closed-loop control / feedback law / a priori estimates / Willett and Wong’s lemma
© EDP Sciences, SMAI 2015