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International Conference on Informatics in Control, Automation and Robotics

ICINCO 2017: Informatics in Control, Automation and Robotics pp 699–718Cite as

On Complementarity Measure-driven Dynamical Systems

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Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 495))

Abstract

We consider a class of complementarity hybrid systems performed by measure differential equations subject to “mixed constraints” on the measure and one-sided limits of the state (prior to and just after the jump). In such systems, vector Borel measures play the role of control inputs/slack variables. We try to understand the asymptotic behavior of solutions to the complementarity problem, namely, look for a constructive representation of the closure of the trajectory funnel. As we invent, a desired representation follows from a particular approximation of solutions and can be described in terms of a specific singular space-time transformation of measure-driven processes. The developed mathematical setup is naturally applied to modeling of Lagrangian systems controlled by instantaneous blocking/releasing a part of its degrees of freedom.

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Acknowledgements

The work is partially supported by the Russian Foundation for Basic Research, grants nos 18-31-20030 and 17-08-00742.

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Authors and Affiliations

  1. Matrosov Institute for System Dynamics and Control Theory of the Siberian Branch of the Russian Academy of Sciences, 134, Lermontov Street, Irkutsk, Russia

    Maxim Staritsyn & Elena Goncharova

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  1. Maxim Staritsyn
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  2. Elena Goncharova
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Correspondence to Maxim Staritsyn .

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Editors and Affiliations

  1. Ford Research and Advanced Engineering, Dearborn, MI, USA

    Oleg Gusikhin

  2. University of Paris-EST Créteil (UPEC), Vitry sur Seine, France

    Kurosh Madani

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Staritsyn, M., Goncharova, E. (2020). On Complementarity Measure-driven Dynamical Systems . In: Gusikhin, O., Madani, K. (eds) Informatics in Control, Automation and Robotics . ICINCO 2017. Lecture Notes in Electrical Engineering, vol 495. Springer, Cham. https://doi.org/10.1007/978-3-030-11292-9_35

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