Singular-perturbation analysis of a closed-loop fixed-end-point optimal-control problem

The closed-loop optimal control of a singularly perturbed system with fixed-end-point conditions results in a special matrix Riccati equation. A singular-perturbation method is presented to analyse the Riccati equation. An algorithm is developed for obtaining the zeroth-, first- and second-order approximate solutions. An illustrative example is given. An integral-squared-error criterion is used to examine the closeness of the approximate solutions.