Singular-perturbation method for discrete models of continuous systems in optimal control

The closed-loop and open-loop optimal controls of a singularly perturbed continuous system are considered by means of their discrete models. A singula-perturbation method is developed to obtain series solutions in terms of the outer, inner and intermediate series analogous to that in a continuous system. It is shown that the resulting matrix Riccati difference equation for closed-loop optimal control is not amenable to singular-perturbation analysis in its original form and has to be properly recast to fit into the framework of singular-perturbation theory. The discrete-model representation has the twin advantages of the reduction in order associated with singular perturbation and the reduction in the computation due to the recursive nature of the solutions in discrete systems. Series solutions are then possible for higher-order approximations with considerable reduction in computation. The method is illustrated by an example.