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We present a scalable reachability algorithm for hybrid systems with piecewise affine, non-deterministic dynamics. It combines poly-hedra and support function representations of continuous sets to compute an over-approximation of the reachable states. The algorithm improves over previous work by using variable time steps to guarantee a given local error(More)
A fundamental question in the treatment of cardiac disorders , such as tachycardia and fibrillation, is under what circumstances does such a disorder arise? To answer to this question, we develop a multiaffine hybrid automaton (MHA) cardiac-cell model, and restate the original question as one of identification of the parameter ranges under which the MHA(More)
This work is concerned with the problem of computing the set of reachable states for linear time-invariant systems with bounded inputs. Our main contribution is a novel algorithm which improves significantly the computational complexity of reachability analysis. Algorithms to compute over and under-approximations of the reachable sets are proposed as well.(More)
In this paper, we are concerned with the problem of computing the reachable sets of hybrid systems with (possibly high dimensional) linear continuous dynamics and guards defined by switching hyperplanes. For the reachability analysis of the continuous dynamics, we use an efficient approximation algorithm based on zonotopes. In order to use this technique(More)
This paper presents a method for using set-based approximations to the Peano-Baker series to compute overapproximations of reachable sets for linear systems with uncertain, time-varying parameters and inputs. Alternative representations for sets of uncertain system matrices are considered, including matrix polytopes, matrix zonotopes, and interval matrices.(More)
We propose a general methodology for approximating the Pareto front of multi-criteria optimization problems. Our search-based methodology consists of submitting queries to a constraint solver. Hence, in addition to a set of solutions , we can guarantee bounds on the distance to the actual Pareto front and use this distance to guide the search. Our(More)
2009 Summary We propose a computer-aided methodology to help analyzing certain biological models Domain of applicability: biochemical reactions modeled as differential equations. State variables denote concentrations We propose reachability computation, a kind of set-based simulation, that may replace uncountably-many simulations The continuous analogue of(More)
In this paper, we present an approximation of the set of reachable states, called flowpipe, for a continuous system with affine dynamics. Our approach is based on a representation we call flowpipe sampling, which consists of a set of continuous, interval-valued functions over time. A flowpipe sampling attributes to each time point a polyhedral enclosure of(More)
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