Optimal control systems governed by nonlinear equations

摘要

We consider a nonlinear control system of the form Av+Fv = BuWe 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. 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.