Abstract
Optimal periodic control problems with integrable or square-integrable control variables are considered. Necessary conditions for optimality, specific features of the set of feasible solutions and the system complex structure are exploited to characterize the smoothness of optimal solutions or all feasible solutions. It is shown that the above devices and the Hardy-Littlewood theorems on Lipschitz classes allow the integral characterization of the control and state continuity for basic practical situations. The importance of such characterization for the trigonometric approximation of optimal periodic control problems is emphasized. The theoretical considerations are illustrated by examples of control problems from the field of chemical engineering.
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