Abstract
Explicit conditions for an improvement in the mean performance using periodic control is presented, and applied to the control of stirred tank reactors. The existence question of a relaxed steady state is dealt with. If an optimal measurable periodic control does not exist, i.e., if the absolute extremum of the objective functional is attained in a relaxed steady state, this fact may also be considered as a result of a technically incorrect or not sound formulation of the mathematical model of the process. It is shown that the introduction of control inertia in the almost general case of practical interest insures the existence of an optimal admissible control, that is, an optimal periodic control which has a finite frequency does not exist. However, the evaluation of the performance of an infinite-frequency control is useful to obtain the upper (or lower) bound of the value of the objective functional. Several examples are given.
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