Singular perturbation method for a closed-loop optimal control problem

The closed-loop optimal control of a singularly perturbed linear system, with free-end-point conditions, gives rise to a matrix Riccati equation. A singular perturbation method is developed to analyse the Riccati equation. An algorithm is presented to indicate the sequence of steps involved in the actual application of the method for obtaining the zeroth-first- and second-order approximations. An example5,6,9 is provided to illustrate the method.