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JOURNALS // Trudy Matematicheskogo Instituta imeni V.A. Steklova // Archive

Trudy Mat. Inst. Steklova, 2010 Volume 271, Pages 93–110 (Mi tm3238)

This article is cited in 6 papers

Hamilton–Jacobi inequalities in control problems for impulsive dynamical systems

V. A. Dykhtaab, O. N. Samsonyukab

a Institute for System Dynamics and Control Theory, Siberian Branch of the Russian Academy of Sciences, Irkutsk, Russia
b Institute of Mathematics, Economics and Information Science, Irkutsk State University, Irkutsk, Russia

Abstract: We propose definitions of strong and weak monotonicity of Lyapunov-type functions for nonlinear impulsive dynamical systems that admit vector measures as controls and have trajectories of bounded variation. We formulate infinitesimal conditions for the strong and weak monotonicity in the form of systems of proximal Hamilton–Jacobi inequalities. As an application of strongly and weakly monotone Lyapunov-type functions, we consider estimates for integral funnels of impulsive systems as well as necessary and sufficient conditions of global optimality corresponding to the approach of the canonical Hamilton–Jacobi theory.

UDC: 517.977.5

Received in February 2010


 English version:
Proceedings of the Steklov Institute of Mathematics, 2010, 271, 86–102

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