On optimal and suboptimal actuator selection strategies

A particular class of optimization problems dealing with the selection, at each instant of time, of one out of many actuators in order to obtain a determined result is studied. A cost is associated with each actuator. The cost function is the integral of a weighted combination of the achieved accuracy on the state of the system and the control energy. The control energy term depends upon both the selected actuator and the magnitude of the applied control. The problem is to design an optimal actuator selection strategy. The analysis is limited to the class of linear deterministic systems with measurable states. A discrete approach is considered. The analytic solution to this optimization problem is given first. When the number of actuators and the number of stages in the time interval become large the optimal analytic solution requires a considerable combinatorial work; a suboptimal algorithm is then proposed to alleviate this defect.