The Experts below are selected from a list of 15345 Experts worldwide ranked by ideXlab platform
Antoine Girard - One of the best experts on this subject based on the ideXlab platform.
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Set Propagation Techniques for Reachability Analysis
Annual Review of Control Robotics and Autonomous Systems, 2021Co-Authors: Matthias Althoff, Goran Frehse, Antoine GirardAbstract:Reachability Analysis consists in computing the set of states that are reachable by a dynamical system from all initial states and for all admissible inputs and parameters. It is a fundamental problem motivated by many applications in formal verification, controller synthesis, and estimation, to name only a few. This paper focuses on a class of methods for computing a guaranteed over-approximation of the reachable set of continuous and hybrid systems, relying predominantly on set propagation: starting from the set of initial states, these techniques iteratively propagate a sequence of sets according to the system dynamics. After a review on set representation and computation, the paper presents the state of the art on set propagation techniques for Reachability Analysis of linear, nonlinear, and hybrid systems. The paper ends with a discussion on successful applications of Reachability Analysis to real world-problems. Contents
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Reachability Analysis of linear systems using support functions
Nonlinear Analysis: Hybrid Systems, 2010Co-Authors: Colas Le Guernic, Antoine GirardAbstract: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 initial states and inputs are given by arbitrary compact convex sets represented by their support functions. We actually compute two over-approximations of the reachable set. The first one is given by the union of convex sets with computable support functions. As the representation of convex sets by their support function is not suitable for some tasks, we derive from this first over-approximation a second one given by the union of polyhedrons. The overall computational complexity of our approach is comparable to the complexity of the most competitive available specialized algorithms for Reachability Analysis of linear systems using zonotopes or ellipsoids. The effectiveness of our approach is demonstrated on several examples.
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Reachability Analysis of Hybrid Systems Using Support Functions
2009Co-Authors: Colas Le Guernic, Antoine GirardAbstract:This paper deals with conservative Reachability Analysis of a class of hybrid systems with continuous dynamics described by linear differential inclusions, convex invariants and guards, and linear reset maps. We present an approach for computing over-approximations of the set of reachable states. It is based on the notion of support function and thus it allows us to consider invariants, guards and constraints on continuous inputs and initial states defined by arbitrary compact convex sets. We show how the properties of support functions make it possible to derive an effective algorithm for approximate Reachability Analysis of hybrid systems. We use our approach on some examples including the navigation benchmark for hybrid systems verification.
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CAV - Reachability Analysis of Hybrid Systems Using Support Functions
Computer Aided Verification, 2009Co-Authors: Colas Le Guernic, Antoine GirardAbstract:This paper deals with conservative Reachability Analysis of a class of hybrid systems with continuous dynamics described by linear differential inclusions, convex invariants and guards, and linear reset maps. We present an approach for computing over-approximations of the set of reachable states. It is based on the notion of support function and thus it allows us to consider invariants, guards and constraints on continuous inputs and initial states defined by arbitrary compact convex sets. We show how the properties of support functions make it possible to derive an effective algorithm for approximate Reachability Analysis of hybrid systems. We use our approach on some examples including the navigation benchmark for hybrid systems verification.
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zonotope hyperplane intersection for hybrid systems Reachability Analysis
ACM International Conference Hybrid Systems: Computation and Control, 2008Co-Authors: Antoine Girard, Colas Le GuernicAbstract: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 for the Analysis of hybrid systems, we must also deal with the discrete transitions in a satisfactory (i.e. scalable and accurate) way. For that purpose, we need to approximate the intersection of the continuous reachable sets with the guards enabling the discrete transitions. The main contribution of this paper is a novel algorithm for computing efficiently a tight over-approximation of the intersection of (possibly high-order) zonotopes with a hyperplane. We show the accuracy and the scalability of our approach by considering two examples of Reachability Analysis of hybrid systems.
Matthias Althoff - One of the best experts on this subject based on the ideXlab platform.
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Set Propagation Techniques for Reachability Analysis
Annual Review of Control Robotics and Autonomous Systems, 2021Co-Authors: Matthias Althoff, Goran Frehse, Antoine GirardAbstract:Reachability Analysis consists in computing the set of states that are reachable by a dynamical system from all initial states and for all admissible inputs and parameters. It is a fundamental problem motivated by many applications in formal verification, controller synthesis, and estimation, to name only a few. This paper focuses on a class of methods for computing a guaranteed over-approximation of the reachable set of continuous and hybrid systems, relying predominantly on set propagation: starting from the set of initial states, these techniques iteratively propagate a sequence of sets according to the system dynamics. After a review on set representation and computation, the paper presents the state of the art on set propagation techniques for Reachability Analysis of linear, nonlinear, and hybrid systems. The paper ends with a discussion on successful applications of Reachability Analysis to real world-problems. Contents
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HSCC - Reachability Analysis for hybrid systems with nonlinear guard sets
Proceedings of the 23rd International Conference on Hybrid Systems: Computation and Control, 2020Co-Authors: Niklas Kochdumper, Matthias AlthoffAbstract:Reachability Analysis is one of the most important methods for formal verification of hybrid systems. The main difficulty for hybrid system Reachability Analysis is to calculate the intersection between reachable set and guard sets. While there exist several approaches for guard sets defined by hyperplanes or polytopes, only few methods are able to handle nonlinear guard sets. In this work we present a novel approach to tightly enclose the intersections of reachable sets with nonlinear guard sets. One major advantage of our method is its polynomial complexity with respect to the system dimension, which makes it applicable for high-dimensional systems. Furthermore, our approach can be combined with different Reachability algorithms for continuous systems due to its modular design. We demonstrate the advantages of our novel approach compared to existing methods with numerical examples.
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Reachability Analysis of large linear systems with uncertain inputs in the krylov subspace
IEEE Transactions on Automatic Control, 2020Co-Authors: Matthias AlthoffAbstract:One often wishes for the ability to formally analyze large-scale systems—typically, however, one can either formally analyze a rather small system or informally analyze a large-scale system. This paper tries to further close this performance gap for Reachability Analysis of linear systems. Reachability Analysis can capture the whole set of possible solutions of a dynamic system and is thus used to prove that unsafe states are never reached; this requires full consideration of arbitrarily varying uncertain inputs, since sensor noise or disturbances usually do not follow any patterns. We use Krylov methods in this paper to compute reachable sets for large-scale linear systems. While Krylov methods have been used before in Reachability Analysis, we overcome the previous limitation that inputs must be (piecewise) constant. As a result, we can compute reachable sets of systems with several thousand state variables for bounded, but arbitrarily varying inputs.
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Reachability Analysis of large linear systems with uncertain inputs in the krylov subspace
arXiv: Numerical Analysis, 2017Co-Authors: Matthias AlthoffAbstract:One often wishes for the ability to formally analyze large-scale systems---typically, however, one can either formally analyze a rather small system or informally analyze a large-scale system. This work tries to further close this performance gap for Reachability Analysis of linear systems. Reachability Analysis can capture the whole set of possible solutions of a dynamic system and is thus used to prove that unsafe states are never reached; this requires full consideration of arbitrarily varying uncertain inputs, since sensor noise or disturbances usually do not follow any patterns. We use Krylov methods in this work to compute reachable sets for large-scale linear systems. While Krylov methods have been used before in Reachability Analysis, we overcome the previous limitation that inputs must be (piecewise) constant. As a result, we can compute reachable sets of systems with several thousand state variables for bounded, but arbitrarily varying inputs, as demonstrated using a bridge model subject to disturbances.
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Reachability Analysis and its application to the safety assessment of autonomous cars
2010Co-Authors: Matthias AlthoffAbstract:This thesis is about the safety verification of dynamical systems using Reachability Analysis. Novel solutions have been developed for classical Reachability Analysis, stochastic Reachability Analysis, and their application to the safety assessment of autonomous cars. Classical Reachability Analysis computes the set of states that can be reached by a system. If the reachable set does not intersect any set of unsafe states, the safety of the system is guaranteed. Algorithms for this problem have been developed for linear, nonlinear, and hybrid systems. Stochastic Reachability Analysis measures the probability of reaching an unsafe set. One pursued approach computes over-approximative solutions for linear systems; another one generates a Markov chain which approximately computes the stochastic reachable set of arbitrary dynamics.
Colas Le Guernic - One of the best experts on this subject based on the ideXlab platform.
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Reachability Analysis of linear systems using support functions
Nonlinear Analysis: Hybrid Systems, 2010Co-Authors: Colas Le Guernic, Antoine GirardAbstract: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 initial states and inputs are given by arbitrary compact convex sets represented by their support functions. We actually compute two over-approximations of the reachable set. The first one is given by the union of convex sets with computable support functions. As the representation of convex sets by their support function is not suitable for some tasks, we derive from this first over-approximation a second one given by the union of polyhedrons. The overall computational complexity of our approach is comparable to the complexity of the most competitive available specialized algorithms for Reachability Analysis of linear systems using zonotopes or ellipsoids. The effectiveness of our approach is demonstrated on several examples.
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Reachability Analysis of Hybrid Systems Using Support Functions
2009Co-Authors: Colas Le Guernic, Antoine GirardAbstract:This paper deals with conservative Reachability Analysis of a class of hybrid systems with continuous dynamics described by linear differential inclusions, convex invariants and guards, and linear reset maps. We present an approach for computing over-approximations of the set of reachable states. It is based on the notion of support function and thus it allows us to consider invariants, guards and constraints on continuous inputs and initial states defined by arbitrary compact convex sets. We show how the properties of support functions make it possible to derive an effective algorithm for approximate Reachability Analysis of hybrid systems. We use our approach on some examples including the navigation benchmark for hybrid systems verification.
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CAV - Reachability Analysis of Hybrid Systems Using Support Functions
Computer Aided Verification, 2009Co-Authors: Colas Le Guernic, Antoine GirardAbstract:This paper deals with conservative Reachability Analysis of a class of hybrid systems with continuous dynamics described by linear differential inclusions, convex invariants and guards, and linear reset maps. We present an approach for computing over-approximations of the set of reachable states. It is based on the notion of support function and thus it allows us to consider invariants, guards and constraints on continuous inputs and initial states defined by arbitrary compact convex sets. We show how the properties of support functions make it possible to derive an effective algorithm for approximate Reachability Analysis of hybrid systems. We use our approach on some examples including the navigation benchmark for hybrid systems verification.
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zonotope hyperplane intersection for hybrid systems Reachability Analysis
ACM International Conference Hybrid Systems: Computation and Control, 2008Co-Authors: Antoine Girard, Colas Le GuernicAbstract: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 for the Analysis of hybrid systems, we must also deal with the discrete transitions in a satisfactory (i.e. scalable and accurate) way. For that purpose, we need to approximate the intersection of the continuous reachable sets with the guards enabling the discrete transitions. The main contribution of this paper is a novel algorithm for computing efficiently a tight over-approximation of the intersection of (possibly high-order) zonotopes with a hyperplane. We show the accuracy and the scalability of our approach by considering two examples of Reachability Analysis of hybrid systems.
Derek Riley - One of the best experts on this subject based on the ideXlab platform.
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Computational methods for Reachability Analysis of stochastic hybrid systems
Lecture Notes in Computer Science, 2006Co-Authors: Xenofon Koutsoukos, Derek RileyAbstract:Stochastic hybrid system models can be used to analyze and design complex embedded systems that operate in the presence of uncertainty and variability. Verification of Reachability properties for such systems is a critical problem. Developing algorithms for Reachability Analysis is challenging because of the interaction between the discrete and continuous stochastic dynamics. In this paper, we propose a probabilistic method for Reachability Analysis based on discrete approximations. The contribution of the paper is twofold. First, we show that Reachability can be characterized as a viscosity solution of a system of coupled Hamilton-Jacobi-Bellman equations. Second, we present a numerical method for computing the solution based on discrete approximations and we show that this solution converges to the one for the original system as the discretization becomes finer. Finally, we illustrate the approach with a navigation benchmark that has been proposed for hybrid system verification.
Radu Grosu - One of the best experts on this subject based on the ideXlab platform.
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Parallel Reachability Analysis of hybrid systems in XSpeed
International Journal on Software Tools for Technology Transfer, 2019Co-Authors: Amit Gurung, Rajarshi Ray, Ezio Bartocci, Sergiy Bogomolov, Radu GrosuAbstract:Reachability Analysis techniques are at the core of the current state-of-the-art technology for verifying safety properties of cyber-physical systems (CPS). The current limitation of such techniques is their inability to scale their Analysis by exploiting the powerful parallel multi-core architectures now available in modern CPUs. Here, we address this limitation by presenting for the first time a suite of parallel state-space exploration algorithms that, leveraging multi-core CPUs, enable to scale the Reachability Analysis for linear continuous and hybrid automaton models of CPS. To demonstrate the achieved performance speedup on multi-core processors, we provide an empirical evaluation of the proposed parallel algorithms on several benchmarks comparing their key performance indicators. This enables also to identify which is the ideal algorithm and the parameters to choose that would maximize the performances for a given benchmark.
