Optimal periodic control: A general theory of necessary conditions

Does time-dependent periodic control yield better process performance than optimal steady, state control? This paper examines exhaustively the role of first order necessary conditions in answering this question. For processes described by autonomous, ordinary differential equations, a very general optimal periodic control problem is formulated. Necessary-conditions are derived for solutions of this problem, steady-state solutions of this problem, and solutions of a related steady-state problem. The relationships between the three sets of necessary conditions and the three sets of solutions is explored extensively. The results integrate and amplify results which have appeared in the literature.