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Verified Probabilistic Reachability in Parametric Hybrid Systems: Theory and Tool Implementation

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Parametric Hybrid Systems (PHS) model systems whose behaviour is mixed continuous/discrete and can depend on parameters which can be stochastic (i.e., random) or nondeterministic (no distribution is known). Such models are useful for describing, e.g., cyber-physical systems and biological systems. In this talk, we present our recent work on bounded probabilistic reachability for PHS . Specifically, we aim at computing the probability that the system reaches a given region of its state space in a given number of discrete steps and finite time. We present an algorithm that is guaranteed to compute an arbitrarily precise approximation of the probability for a reasonably large class of PHS (so-called robust systems). The algorithm has been implemented in the ProbReach tool, which is available at https://github.com/dreal/probreach. As an application example we describe the synthesis of safe PID (Proportional Integral Derivative) controllers for the artificial pancreas.

This talk is part of the Computer Laboratory Wednesday Seminars series.

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