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The maximum principle for variable structure systems. (English) Zbl 1077.93011
Summary: In this article we consider Mayer and Lagrange optimization problems for controlled variable structure systems (VSS). We prove the maximum principle as a necessary condition of optimality. The principle includes a new form of the jump condition. In the proofs we use the tent method that was worked out by {\it V. G. Boltyanskij} [Usp. Mat. Nauk 30, No. 3 (183), 3--55 (1975; Zbl 0318.49017); see also the first chapter in {\it V. Boltyanski, H. Martini} and {\it V. Soltan}, Geometric methods and optimization problems. Dordrecht: Kluwer Academic Publishers (1999; Zbl 0933.90002)].

93B12Variable structure systems
49K15Optimal control problems with ODE (optimality conditions)
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