Optimal control system design: The control and sampling problem

An extended formulation of the optimal control problem is proposed that assesses system performance using a performance index that measures both control performance and the costs for implementing the control law. This extended problem formulation is illustrated by the control and sampling problem, where the sampling times at which measurements are taken and control commands dispatched are control variables. The control law is thus determined by selecting the number of sampling times, the length of sampling intervals, and the levels of each control element during each sampling interval. The optimal control system design is proved to approach the optimal continuous-time control for the special case where the cost of implementation is negligible and the number of sampling times can be arbitrarily large. The optimal control system design is shown to approach the optimal periodic sampled-data control when the costs of implementation are very large and have a particular form.