Lagrangian Reachabililty

Cyranka, Jacek; Islam, Md. Ariful; Byrne, Greg; Jones, Paul; Smolka, Scott A.; Grosu, Radu

doi:10.1007/978-3-319-63387-9_19

Cited by 9 publications

(35 citation statements)

References 27 publications

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“…The LRT algorithm computes a conservative, discrete-time reachtube for nonlinear, time-variant dynamical systems, based on finite strain theory [8].…”

Section: B Review Of the Lrt Algorithmmentioning

confidence: 99%

“…FTLE is used e.g, in climate research to detect Lagrangian-coherent structures [23]. The correctness of the LRT algorithm is given by the following theorem [8].…”

Section: B Review Of the Lrt Algorithmmentioning

confidence: 99%

“…Recent work introduced Lagrangian ReachTube algorithm (LRT), a new approach for the reachability analysis of continuous, nonlinear, dynamical systems [8]. LRT constructs a discrete-time reachtube (or flowpipe) that given a dynamical system, tightly overestimates the set of reachable states at each time point.…”

Section: Introductionmentioning

confidence: 99%

“…We also provide a very concise proof of this fact. Moreover, using SDP significantly increases the running time of the algorithm (compared to the approach based on analytical formulas), and can result in numerical instabilities (refer to the discussion in [8]) and excessive bloating.…”

Section: Introductionmentioning

confidence: 99%

“…We have implemented a prototype of CLRT in C++ and thoroughly investigated its performance on a set of benchmarks, including those used in [8]. Our results show that compared to CAPD, CLRT performs favorably in terms of the continuous-reachtube volumes they compute.…”

Section: Introductionmentioning

confidence: 99%

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Tight Continuous-Time Reachtubes for Lagrangian Reachability

Cyranka

Islam

Smolka

et al. 2018

2018 IEEE Conference on Decision and Control (CDC)

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We introduce continuous Lagrangian reachability (CLRT), a new algorithm for the computation of a tight and continuous-time reachtube for the solution flows of a nonlinear, time-variant dynamical system. CLRT employs finite strain theory to determine the deformation of the solution set from time ti to time ti+1. We have developed simple explicit analytic formulas for the optimal metric for this deformation; this is superior to prior work, which used semi-definite programming. CLRT also uses infinitesimal strain theory to derive an optimal time increment hi between ti and ti+1, nonlinear optimization to minimally bloat (i.e., using a minimal radius) the state set at time ti such that it includes all the states of the solution flow in the interval [ti, ti+1]. We use δ-satisfiability to ensure the correctness of the bloating. Our results on a series of benchmarks show that CLRT performs favorably compared to state-of-the-art tools such as CAPD in terms of the continuous reachtube volumes they compute. * Jacek Cyranka and Md. Ariful Islam contributted equally to this work.

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“…The LRT algorithm computes a conservative, discrete-time reachtube for nonlinear, time-variant dynamical systems, based on finite strain theory [8].…”

Section: B Review Of the Lrt Algorithmmentioning

confidence: 99%

“…FTLE is used e.g, in climate research to detect Lagrangian-coherent structures [23]. The correctness of the LRT algorithm is given by the following theorem [8].…”

Section: B Review Of the Lrt Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Tight Continuous-Time Reachtubes for Lagrangian Reachability

Cyranka

Islam

Smolka

et al. 2018

2018 IEEE Conference on Decision and Control (CDC)

Self Cite

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Piecewise Robust Barrier Tubes for Nonlinear Hybrid Systems with Uncertainty

Kong

Bartocci

Jiang

et al. 2019

Lecture Notes in Computer Science

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Piecewise Barrier Tubes (PBT) is a new technique for flowpipe overapproximation for nonlinear systems with polynomial dynamics, which leverages a combination of barrier certificates. PBT has advantages over traditional time-step based methods in dealing with those nonlinear dynamical systems in which there is a large difference in speed between trajectories, producing an overapproximation that is time independent. However, the existing approach for PBT is not efficient due to the application of interval methods for enclosure-box computation, and it can only deal with continuous dynamical systems without uncertainty. In this paper, we extend the approach with the ability to handle both continuous and hybrid dynamical systems with uncertainty that can reside in parameters and/or noise. We also improve the efficiency of the method significantly, by avoiding the use of interval-based methods for the enclosure-box computation without loosing soundness. We have developed a C++ prototype implementing the proposed approach and we evaluate it on several benchmarks. The experiments show that our approach is more efficient and precise than other methods in the literature. arXiv:1907.11514v1 [eess.SY]

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NeuReach: Learning Reachability Functions from Simulations

Sun

Mitra

2022

Lecture Notes in Computer Science

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We present , a tool that uses neural networks for predicting reachable sets from executions of a dynamical system. Unlike existing reachability tools, computes a reachability function that outputs an accurate over-approximation of the reachable set for any initial set in a parameterized family. Such reachability functions are useful for online monitoring, verification, and safe planning. implements empirical risk minimization for learning reachability functions. We discuss the design rationale behind the optimization problem and establish that the computed output is probably approximately correct. Our experimental evaluations over a variety of systems show promise. can learn accurate reachability functions for complex nonlinear systems, including some that are beyond existing methods. From a learned reachability function, arbitrary reachtubes can be computed in milliseconds. is available at https://github.com/sundw2014/NeuReach.

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Lagrangian Reachabililty

Cited by 9 publications

References 27 publications

Tight Continuous-Time Reachtubes for Lagrangian Reachability

Tight Continuous-Time Reachtubes for Lagrangian Reachability

Piecewise Robust Barrier Tubes for Nonlinear Hybrid Systems with Uncertainty

NeuReach: Learning Reachability Functions from Simulations

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