Optimal Control for Time Delay Singular Systems

For the class of singular time-delay dynamical systems we present optimal control results. We developed 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 time-delay system. Furthermore, the Lyapunov function is shown to be a solution of a steady-state, Hamilton-Jacobi-Bellman equation.