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The reachable sets concept applied to a class of min-max optimization problems

Terlikowski T.

Archives of Control Sciences

2003

Vol. 13, no. 1

47-58

A multi-criteria control problem over the infinite time horizon for periodical system is considered. our aim is solve problems of type using the known idea of reachable sets. The worst case approach applied concerns e.g. a system of water resources distribution. The min-max opimisation problem obtained occurs to fit naturally the scheme of reachable sets concept. applicability of this concept to that particular case is discussed and the algorithm is presented.

Solution tubes to differential inclusions within a collection of sets

Quincampoix M., Veliov V.

Control and Cybernetics

2002

Vol. 31, no 3

847-862

This paper develops the theory of solution tubes to differential inclusions (uncertain systems) within a prescribed collection of sets. The notion is defined as a minimal invariant tube with values in the collection. Under certain requirements for the collection we prove existence and Lipschitz-like stability of the solution tubes. The theory is relevant to problems of systems estimation in the context of control or differential games.