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Hybrid Control Systems Using Timed Petri Nets: Supervisory Control Design Based on Invariant Properties

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Hybrid Systems V (HS 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1567))

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Abstract

In this paper, a class of timed Petri nets named programmable timed Petri nets is used for supervisory control of hybrid systems. In particular, the transfer of the continuous state to a region of the state space under safety specifications on the discrete and continuous dynamics is addressed. The switching policy is embedded in the dynamics of the underlying Petri net structure and the supervisors are described by Petri nets. The discrete specifications are expressed in terms of linear constraints on the marking vector and are satisfied by applying supervisory control of Petri nets based on place invariants. The hybrid system switches from a subsystem to another, in a way that the state gradually progresses from one equilibrium to another towards the desired target equilibrium. The supervisory control algorithm is designed to allow switchings to occur only on the intersection of the invariant manifolds. Finally, in the case when the continuous dynamics are described by first order integrators, the design algorithm is formulated as a linear programming problem.

This work was supported in part by the National Science Foundation grant ECS95-31485.

This author gratefully acknowledges the fellowship of the Center of Applied Mathematics at the University of Notre Dame for the academic year 1997–98.

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Authors and Affiliations

  1. Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN, 46556, USA

    Xenofon D. Koutsoukos & Panos J. Antsaklis

Authors
  1. Xenofon D. Koutsoukos
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  2. Panos J. Antsaklis
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Editor information

Editors and Affiliations

  1. Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN, 46556, USA

    Panos Antsaklis  & Michael Lemmon  & 

  2. Hynomics Corporation, 10632 NE 37th Circle, Building 23, Kirkland, WA, 98033, USA

    Wolf Kohn

  3. Department of Mathematics, Cornell University, 217, White Hall, Ithaca, NY, 14853, USA

    Anil Nerode

  4. Electronic Research Laboratory, University of California at Berkeley, 253 Cory Hall, Berkeley, CA, 94720, USA

    Shankar Sastry

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© 1999 Springer-Verlag Berlin Heidelberg

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Koutsoukos, X.D., Antsaklis, P.J. (1999). Hybrid Control Systems Using Timed Petri Nets: Supervisory Control Design Based on Invariant Properties. In: Antsaklis, P., Lemmon, M., Kohn, W., Nerode, A., Sastry, S. (eds) Hybrid Systems V. HS 1997. Lecture Notes in Computer Science, vol 1567. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49163-5_8

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  • DOI: https://doi.org/10.1007/3-540-49163-5_8

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  • Print ISBN: 978-3-540-65643-2

  • Online ISBN: 978-3-540-49163-7

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