Chapter

Hybrid Systems: Computation and Control

Volume 3927 of the series Lecture Notes in Computer Science pp 4-18

Behavioural Approximations for Restricted Linear Differential Hybrid Automata

  • Manindra AgrawalAffiliated withDepartment of Computer Science and Engineering, Indian Institute of Technology
  • , Frank StephanAffiliated withSchool of Computing and Department of Mathematics, National University of Singapore (NUS)
  • , P. S. ThiagarajanAffiliated withSchool of Computing, National University of Singapore
  • , Shaofa YangAffiliated withSchool of Computing, National University of Singapore

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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.