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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)
— Set-based reachability analysis computes all possible states a system may attain, and in this sense provides knowledge about the system with a completeness, or coverage, that a finite number of simulation runs can not deliver. Due to its inherent complexity, the application of reachability analysis has been limited so far to simple systems, both in the(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 work is concerned with the algorithmic reachability analysis of continuous-time linear systems with constrained initial states and inputs. We propose an approach for computing an over-approximation of the set of states reachable on a bounded time-interval. The main contribution over previous works is that it allows us to consider systems whose sets of(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)
In this paper we describe reachability computation for continuous and hybrid systems and its potential contribution to the process of building and debugging biological models. We summarize the state-of-the-art for linear systems and then develop a novel algorithm for computing reachable states for nonlinear systems. We report experimental results obtained(More)