Policy iteration-based optimal control design for nonlinear descriptor systems

This paper considers state feedback optimal control design for a class of nonlinear descriptor systems. Prior work either stops at the Hamilton-Jacobian-Bellman equations and thus is non-constructive, or converts the optimal control problem into a large scale nonlinear optimization problem and thus is open-loop control design. This paper proposes a generalized policy iteration algorithm to compute the state feedback optimal control policy in a constructive manner, and presents the convergence analysis. Compared with the conventional one for systems in a classic state space form, the generalized policy iteration algorithm for nonlinear descriptor systems differs in the presence of an extra partial differential equation system from which the value function is solved. Necessary and sufficient conditions guaranteeing solvability of the value function are established. Sufficient solvability conditions for a special case, where the value function is a linear combination of a set of basis functions, are also derived.