On BV-extension of asymptotically constrained control-affine systems and complementarity problem for measure differential equations

Elena Goncharova; Maxim Staritsyn

doi:10.3934/dcdss.2018061

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2018, Volume 11, Issue 6: 1061-1070. Doi: 10.3934/dcdss.2018061

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On BV-extension of asymptotically constrained control-affine systems and complementarity problem for measure differential equations

Elena Goncharova and
Maxim Staritsyn

Institute for System Dynamics and Control Theory, Siberian Branch of the Russian Academy of Sciences, Irkutsk, Russia

Received: February 28, 2017

Revised: May 31, 2017

Published: December 2018

The work was partially supported by the Russian Foundation for Basic Research, projects 16-08-00272, 16-31-60030, 16-31-00184, 17-08-00742

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The goal of the paper is to design a constructive impulsive trajectory extension for a class of control-affine dynamical systems subject to a asymptotic mixed constraint of complementarity type. An inspiration for the addressed models comes from the framework of Lagrangian mechanical systems with impactively blockable degrees of freedom. The constraint formalizes the requirement that "control actions steer the system's state from one prescribed configuration $\mathcal{Z}_-$ to another one $\mathcal{Z}_+$". This issue is also closely connected with the problem of continuous trajectory approximation of hybrid systems with control switches.

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Mathematics Subject Classification: Primary: 49N25, 49K99; Secondary: 49J99.

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