Uniformly valid feedback expansions for optimal control of singularly perturbed dynamic systems (Q799559)

This paper shows how to construct a feedback control law for a class of singularly perturbed autonomous optimization problems. The control law is expressed as a single power series in the small parameter \(\epsilon\) representing the ratio of the two effective time scales of the problem. The present approach avoids the need of expansion matching; however, equivalence with the technique of matched asymptotic expansions is demonstrated. The method is applied to a constant-speed interception problem. Comparison of numerical results with the exact solution shows an excellent agreement.