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Extracting counterexamples induced by safety violation in linear hybrid systems. (English) Zbl 1442.93020
Summary: Control design for linear systems typically involves pole placement and computing Lyapunov functions. While these tools are useful for ensuring stability, they are not always helpful in ensuring safety. Control designers can employ model checking as a tool for checking safety. We believe that supplementing the model checker to provide various types of counterexamples for the safety specification would help the control designer in the control development process. In this paper, we describe a technique for obtaining the variety of counterexamples for a safety violation in linear hybrid systems. More specifically, we develop algorithms to extract the longest counterexample – the execution that stays in the unsafe set for the longest contiguous time, deepest counterexample – the execution that ventures the most into the unsafe set in a user specified direction, and the robust counterexample – the unsafe execution from which some bounded perturbation yields a new counterexample. These measures for classifying counterexamples can further assist in quantifying controllers’ performance.
MSC:
93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
93B55 Pole and zero placement problems
93C05 Linear systems in control theory
90C05 Linear programming
90C39 Dynamic programming
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