Optimal control during feedback failure

The problem of controlling a perturbed open loop system so as to keep its performance errors within bounds is considered. The objective is to maximize the time during which performance errors remain below a prescribed ceiling, while the controlled system’s parameters are within a specified neighborhood of their nominal values. It is shown that there is an optimal open-loop controller that achieves this objective. Conditions under which the optimal controller generates a bang-bang control input signal are characterized. In general, it is shown that the performance of the optimal controller can always be approximated by a bang-bang signal.