Partial Differential Inclusions Governing Feedback Controls

Aubin, J.-P. & Frankowska, H. (1990). Partial Differential Inclusions Governing Feedback Controls. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-90-028

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Abstract

The authors derive partial differential inclusions of hyperbolic type, the solutions of which are feedbacks governing the viable (controlled invariant) solutions of a control system. They show that the tracking property, another important control problem, leads to such hyperbolic systems of partial differential inclusions. They begin by proving the existence of the largest solution of such a problem, a stability result and provide an explicit solution in the particular case of decomposable systems. They then state a variational principle and an existence theorem of a. (single-valued contingent) solution to such an inclusion, that they apply to assert the existence of a feedback control.

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