Behavioural Approximations for Restricted Linear Differential Hybrid Automata

  • Manindra Agrawal
  • Frank Stephan
  • P. S. Thiagarajan
  • Shaofa Yang
Conference paper

DOI: 10.1007/11730637_4

Part of the Lecture Notes in Computer Science book series (LNCS, volume 3927)
Cite this paper as:
Agrawal M., Stephan F., Thiagarajan P.S., Yang S. (2006) Behavioural Approximations for Restricted Linear Differential Hybrid Automata. In: Hespanha J.P., Tiwari A. (eds) Hybrid Systems: Computation and Control. HSCC 2006. Lecture Notes in Computer Science, vol 3927. Springer, Berlin, Heidelberg

Abstract

We show the regularity of the discrete time behaviour of hybrid automata in which the rates of continuous variables are governed by linear differential operators in a diagonal form and in which the values of the continuous variables can be observed only with finite precision. We do not demand resetting of the values of the continuous variables during mode changes. We can cope with polynomial guards and we can tolerate bounded delays both in sampling the values of the continuous variables and in effecting changes in their rates required by mode switchings. We also show that if the rates are governed by diagonalizable linear differential operators with rational eigenvalues and there is no delay in effecting rate changes, the discrete time behaviour of the hybrid automaton is recursive. However, the control state reachability problem in this setting is undecidable.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Manindra Agrawal
    • 1
  • Frank Stephan
    • 2
  • P. S. Thiagarajan
    • 3
  • Shaofa Yang
    • 3
  1. 1.Department of Computer Science and EngineeringIndian Institute of TechnologyKanpurIndia
  2. 2.School of Computing and Department of MathematicsNational University of Singapore (NUS)Singapore
  3. 3.School of ComputingNational University of SingaporeSingapore

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