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Decidable Controller Synthesis for Classes of Linear Systems

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Hybrid Systems: Computation and Control (HSCC 2000)

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Abstract

A problem of great interest in the control of hybrid systems is the design of least restrictive controllers for reachability specifications. Controller design typically uses game theoretic methods which compute the region of the state space for which there exists a control such that for all disturbances, an unsafe set is not reached. In general, the computation of the controllers requires the steady state solution of a Hamilton-Jacobi-Isaacs partial differential equation which is very difficult to compute, if it exists. In this paper, we show that for classes of linear systems, the controller synthesis problem is decidable: There exists a computational algorithm which, after a finite number of steps, will exactly compute the least restrictive controller. This result is achieved by a very interesting interaction of results from mathematical logic and optimal control.

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Author information

Authors and Affiliations

  1. Department of EECS, University of California at Berkeley, Berkeley, CA, 94704

    Omid Shakernia, George J. Pappas & Shankar Sastry

  2. Department of CIS, University of Pennsylvania, Philadelphia, PA, 19104

    George J. Pappas

Authors
  1. Omid Shakernia
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  2. George J. Pappas
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  3. Shankar Sastry
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Editor information

Editors and Affiliations

  1. Laboratory for Computer Science, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

    Nancy Lynch

  2. Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA, 15235, USA

    Bruce H. Krogh

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© 2000 Springer-Verlag Berlin Heidelberg

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Shakernia, O., Pappas, G.J., Sastry, S. (2000). Decidable Controller Synthesis for Classes of Linear Systems. In: Lynch, N., Krogh, B.H. (eds) Hybrid Systems: Computation and Control. HSCC 2000. Lecture Notes in Computer Science, vol 1790. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46430-1_34

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  • DOI: https://doi.org/10.1007/3-540-46430-1_34

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67259-3

  • Online ISBN: 978-3-540-46430-3

  • eBook Packages: Springer Book Archive

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