A Stability Theorem for Constrained Optimal Control Problems (Journal of Computational Mathematics, 2004)
This paper presents the stability of difference approximations of an optimal control problem for a quasilinear parabolic equation with controls in the coefficients, boundary conditions and additional restrictions. The optimal control problem has been converted to one of the optimization problem using a penalty function technique. The difference approximations problem for the considered problem is obtained. The estimations of stability of the solution of difference approximations problem are proved. The stability estimation of the solution of difference approximations problem by the controls is obtained.
Keywords: Optimal control; Quasilinear Parabolic equations; Penalty function methods; Finite difference method; Stability estimations.