Legendre-Tau Approximation for Functional Differential Equations Part II: The Linear Quadratic Optimal Control Problem

A numerical scheme based on the Legendre-tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems. The convergence property is established using the Trotter–Kato theorem. The method yields very good approximations at low orders and provides an approximation technique for computing closed-loop eigenvalues of the feedback system. A comparison with existing methods (based on “averaging” and “spline” approximations) is made.