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The Discrete Time Behaviour of Restricted Linear Hybrid Automata
(2008-12-15T01:59:32Z) AGRAWAL, Manindra; STEPHAN, Frank; THIAGARAJAN, P. S.; YANG, Shaofa
We summarize results from [2, 3, 1] on the discrete time behaviour of a class of restricted linear hybrid automata. Specifically, we show the regularity of the discrete time behaviour of hybrid automata in which the rates of continuous vari- ables are governed by linear operators in a diagonal form and in which the values of the continuous variables can be observed only with finite precision. Crucially, we do not demand—as is usually done—that the values of the continuous vari- ables be reset 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 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.