Variational Inequality Approach To Optimal Control Problems With Joint State-Control Constraints

Optimal control problem(OCP)with joint state-control constraint is studied.It is shown that a state-control pair solves the OCP if and only if it satisfies a differential quasi variational inequality(DQVI),which consists of an Hamilton equation and the optimality condition of a minimization.The DQVI is then reformulated into an infinitedimensional variational inequality(VI).Monotone and coercive properties of the VI are investigated,these properties are utilized to establish the solvability of the OCP.Finally a regularized Galerkin method is proposed,which approximates the least norm solution of the OCP by solving finite-dimensional VIs that are strongly monotone.The convergence conditions are natural and mild in comparison with those existing.