Optimal Control of Singular Systems. Continuous Time Case

In this paper for the class of singular dynamical systems we present optimal control results. We develop unified framework for feedback optimal and inverse optimal control involving a nonlinear-nonquadratic performance functional. It is shown that the cost functional can be evaluated in closed-form as long as the cost functional considered is related in a specific way to an underlying Lyapunov function that guarantees asymptotic stability of the nonlinear closed-loop singular system. Furthermore, the Lyapunov function is shown to be a solution of a steady-state, Hamilton-Jacobi-Bellman equation.