The linear quadratic optimal control problem for hereditary differential systems: Theory and numerical solution

Abstract

In the first part of this paper, we summarize and complete earlier results of Delfour-Mitter [3] on the optimal control problem for linear hereditary differential systems (HDS) with a linear-quadratic cost function. The properties of the operator Π(t) which characterizes the feedback gains and the reference functionr(t) are fully detailed. In a second part, we construct an approximation to the linear HDS in state form and to the linear adjoint state equation and prove convergence. In a third part we construct and solve the approximate optimal control problem following the method of J. C. Nedelec. In the last part we construct the approximation to Π(t) andr(t) and prove convergence. Finally we give a number of typical examples to illustrate the main features of the kernel of Π(t).