EXISTENCE OF OPTIMAL CONTROLS FOR CONTINUOUS-TIME INFINITE-HORIZON PROBLEMS

An existence theorem is given for general continuous time infinite hor izon optimal control formulations. Specifically, we establish conditio ns on the plant model, the cost integrand and the set of initial state s to be considered under which the infinite horizon optimal control pr oblem has a solution. The conditions on the objective function are of a sufficiently general nature to allow flexibility in the choice of co st function and therefore the hypotheses easily fit standard process s ystems applications.