Multiple Stage Optimal Control Problems with Applications to Plasma Heating by Neutral Injection.

Abstract
Three classes of multiple stage optimal control problems are studied. The derived results are applied to the problem of toroidal plasma heating by means of neutral injection. First a two-stage optimal control problem having an integral cost functional, whose integrand changes its form at an unspecified switching time, is considered. An existence theorem and two sets of necessary conditions for an optimal control and switching time are derived for a general two-stage problem. The optimal heating problem is reformulated as a multi-stage optimal control problem using a single-temperature model of the plasma. The optimal heating program is shown to assume one of three possible on-off forms, depending on the heating time duration. Finally, the stability of two classes of ion temperature feedback control systems is discussed. The results suggest the possibility of regulation of the ion temperature using feedback-controlled neutral injection.

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