An Iterative Solution to the Finite-Time Linear Quadratic Optimal Feedback Control Problem

Saridis's successive approximation theory is applied to the finite-time linear quadratic optimal control problem. The result is an iterative scheme which successively improves any initial control law ultimately converging to the optimal state feedback control. The novelty of the approach is that the solution of a nonlinear Riccati equation is replaced by the successive solution to a linear Lyapunov equation. Numerical examples illustrate the approach.