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ON EXTERNAL PENALTY FUNCTIONS APPROACH IN REACHABILITY ANALYSIS UNDER PIECEWISE SMOOTH STATE CONSTRAINTS

Annotation

The paper is devoted to the problem of external approximating trajectory tubes of a control system with state constraints. An analog of external penalty function method which consists in replacing the primary system by auxiliary system without state constraints is proposed.

Keywords

control system; trajectory tube; reachable set; state constraints; penalty function method

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UDC

517.977.1

Pages

1122-1124

References

1. Bressan A., Facchi G. Trajectories of differential inclusions with State Constraints // J. Differential Equations. 2011. V. 250. № 2. P. 2267–2281. 2. Gusev M.I. Vnutrennie approksimatsii mnozhestv dostizhimosti nelineynykh upravlyaemykh sistem s fazovymi ogranicheniyami // Vestnik Tambovskogo universiteta. Seriya Estestvennye i tekhnicheskie nauki. Tambov, 2013. T. 18. Vyp. 5. S. 2498–2500. 3. Gusev M.I. Vnutrennie approksimatsii mnozhestv dostizhimosti upravlyaemykh sistem s fazovymi ogranicheniyami // Tr. In-ta matematiki i mekhaniki UrO RAN. Ekaterinburg, 2013. T. 19. № 4. S. 73–88. 4. Sontag E.D. A ’universal’ construction of Artstein’s theorem on nonlinear stabilization// System and Control Letters. 1989. V. 13. P. 117–123.

Received

2015-04-27

Section of issue

Scientific articles

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