Optimal control systems governed by nonlinear equations

Abstract

We consider a nonlinear control system of the form $$Av + Fv = Bu$$ along with observation equation $$z(u) = Cv(u)$$ Here A, B, C are linear operators and F is a nonlinear operator in appropriate spaces. u is a control variable and v is the state of the system corresponding to u. Under continuity and monotonicity assumptions on A, B, C and F, we obtain a minimizer of a functional J in a constrained set as a limit of a sequence of unconstrained minimizers of J.