Dynamic selection of actuators for lumped and distributed parameter systems

The theory of relaxed controls is used to solve the problem of selection, at each instant of time, of one out of many actuators in order to obtain a desired result. For lumped parameter systems it is shown that there exist optimal solutions for the problem involving the minimization of a quadratic cost functional. Necessary conditions for optimality are established and a numerical algorithm to determine the optimal solution is proposed. The method developed for lumped parameter systems is extended to distributed systems and, in particular, to the problem of Optimal allocation of actuators.