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Sliding Modes and Lyapunov Functions for Differential Inclusions by Linear Programming

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Informatics in Control, Automation and Robotics (ICINCO 2020)

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 793))

Abstract

Recently the concept of essential neighbours of simplices was introduced for switched systems and differential inclusions with triangulated state spaces. It was used to design an algorithm that was able to compute Lyapunov functions for such systems with a strongly asymptotically stable equilibrium, of which the Filippov regularization does not have a strongly asymptotically stable equilibrium. Here we advance this algorithm further and show that the methodology can additionally be used to localize the sliding modes is differential inclusions. Using this localization we can remove constraints from a linear programming problem, whose feasible solutions parameterize Lyapunov functions for the system. We demonstrate the efficacy of our new approach for three systems from the literature.

This research was supported by the Icelandic Research Fund (Rannís) grant number 163074-052, Complete Lyapunov functions: Efficient numerical computation.

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Authors and Affiliations

  1. Science Institute, University of Iceland, Dunhagi 5, 107, Reykjavík, Iceland

    Sigurdur Hafstein

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  1. Sigurdur Hafstein
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Correspondence to Sigurdur Hafstein .

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

    Oleg Gusikhin

  2. University Paris-Est Créteil (UPEC), Créteil, France

    Kurosh Madani

  3. University of Reims Champagne-Ardenne, Reims, France

    Janan Zaytoon

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Hafstein, S. (2022). Sliding Modes and Lyapunov Functions for Differential Inclusions by Linear Programming. In: Gusikhin, O., Madani, K., Zaytoon, J. (eds) Informatics in Control, Automation and Robotics. ICINCO 2020. Lecture Notes in Electrical Engineering, vol 793. Springer, Cham. https://doi.org/10.1007/978-3-030-92442-3_29

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