On the set of attainability of nonlinear autonomous control systems

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An important tool in optimal control theory is the Pontrjagin maximum principle. A necessary condition for optimality, the principle is an analytic description of a control whose response stays in the boundary of the attainable set. See[2, 21]. It is useful to know that the attainable set has nonempty interior because the maximum principle gives no information otherwise. If we consider nonlinear, autonomous control systems determined on a manifold M by the set ℳk of autonomous, Ck controllable vector fields, then a few technical restrictions on the control system allow us to conclude that there is an open dense subset O of ℳk such that each element of O has an attainable set contained in the closure of its own interior.


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Entrata in Redazione il 20 novembre 1974.

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Rebhuhn, D. On the set of attainability of nonlinear autonomous control systems. Annali di Matematica 107, 291–309 (1975) doi:10.1007/BF02416478

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  • Control System
  • Vector Field
  • Control Theory
  • Controllable Vector
  • Maximum Principle