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Efficient reachability analysis of parametric linear hybrid systems with time-triggered transitions

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Document pages: 17 pages

Abstract: Efficiently handling time-triggered and possibly nondeterministic switchesfor hybrid systems reachability is a challenging task. In this paper we presentan approach based on conservative set-based enclosure of the dynamics that canhandle systems with uncertain parameters and inputs, where the uncertaintiesare bound to given intervals. The method is evaluated on the plant model of anexperimental electro-mechanical braking system with periodic controller. Inthis model, the fast-switching controller dynamics requires simulation timescales of the order of nanoseconds. Accurate set-based computations forrelatively large time horizons are known to be expensive. However, byappropriately decoupling the time variable with respect to the spatialvariables, and enclosing the uncertain parameters using interval matrix mapsacting on zonotopes, we show that the computation time can be lowered to 5000times faster with respect to previous works. This is a step forward in formalverification of hybrid systems because reduced run-times allow engineers tointroduce more expressiveness in their models with a relatively inexpensivecomputational cost.

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