Safety verification and reachability analysis for hybrid systems

Guéguen, Hervé; Lefebvre, Marie-Anne; Nasri, Othman; Zaytoon, Janan

doi:10.3182/20080706-5-kr-1001.01512

Cited by 11 publications

(13 citation statements)

References 18 publications

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“…An alternative, indirect method relies on the numerical computation of the zero-level set of the viscosity solution of the Hamilton-Jacobi-Bellman equations, though with exponential time complexity [2]. Modern research on reachability analysis has therefore focused on producing efficient overor under-approximations of reachable sets and has progressed from the continuous-time linear case [5], to general nonlinear dynamics [6], [7], to nonlinear differential-algebraic dynamics [8] and hybrid systems [9]. These techniques have been tailored to specific applications such as spacecraft dynamics [10] and aircraft dynamics.…”

Section: Introductionmentioning

confidence: 99%

A machine learning approach for real-time reachability analysis

Allen

Clark

Starek

et al. 2014

2014 IEEE/RSJ International Conference on Intelligent Robots and Systems

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Assessing reachability for a dynamical system, that is deciding whether a certain state is reachable from a given initial state within a given cost threshold, is a central concept in controls, robotics, and optimization. Direct approaches to assess reachability involve the solution to a two-point boundary value problem (2PBVP) between a pair of states. Alternative, indirect approaches involve the characterization of reachable sets as level sets of the value function of an appropriate optimal control problem. Both methods solve the problem accurately, but are computationally intensive and do no appear amenable to real-time implementation for all but the simplest cases. In this work, we leverage machine learning techniques to devise querybased algorithms for the approximate, yet real-time solution of the reachability problem. Specifically, we show that with a training set of pre-solved 2PBVP problems, one can accurately classify the cost-reachable sets of a differentially-constrained system using either (1) locally-weighted linear regression or (2) support vector machines. This novel, query-based approach is demonstrated on two systems: the Dubins car and a deepspace spacecraft. Classification errors on the order of 10% (and often significantly less) are achieved with average execution times on the order of milliseconds, representing 4 orders-ofmagnitude improvement over exact methods. The proposed algorithms could find application in a variety of time-critical robotic applications, where the driving factor is computation time rather than optimality. the

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Section: Introductionmentioning

confidence: 99%

A machine learning approach for real-time reachability analysis

Allen

Clark

Starek

et al. 2014

2014 IEEE/RSJ International Conference on Intelligent Robots and Systems

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“…Viability kernels can be approximated for linear systems, for example, by using analysis of random directions in the state space [35]. Reachability analysis of hybrid systems has also been extensively researched in the last 20 years [36]. Reachability analysis tools exist for classes of systems with timed [37], rectangular [38], [39], linear [17], [39], and nonlinear [40], [41] dynamics, with varying degrees of accuracy and scalability.…”

Section: Related Workmentioning

confidence: 99%

Real-Time Reachability for Verified Simplex Design

Bak

Johnson

Caccamo

et al. 2014

2014 IEEE Real-Time Systems Symposium

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The Simplex Architecture ensures the safe use of an unverifiable complex controller by using a verified safety controller and verified switching logic. This architecture enables the safe use of high-performance, untrusted, and complex control algorithms without requiring them to be formally verified. Simplex incorporates a supervisory controller and safety controller that will take over control if the unverified logic misbehaves. The supervisory controller should (1) guarantee the system never enters and unsafe state (safety), but (2) use the complex controller as much as possible (minimize conservatism).The problem of precisely and correctly defining this switching logic has previously been considered either using a controltheoretic optimization approach, or through an offline hybrid systems reachability computation. In this work, we prove that a combined online/offline approach, which uses aspects of the two earlier methods along with a real-time reachability computation, also maintains safety, but with significantly less conservatism. We demonstrate the advantages of this unified approach on a saturated inverted pendulum system, where the usable region of attraction is 227% larger than the earlier approach.

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“…Then there is a function f that satisfies (1) if and only if the system is safe. Constraint (2) implies that the vector field ξ has no singular points in X.…”

Section: Introductionmentioning

confidence: 96%

“…Numerous efforts have been conducted for developing safety verification of continuous systems [1]; however, the complexity of the verification is usually very high. Therefore, resent research efforts have been mainly concerned with complexity reduction and development of scalable algorithms for tool implementations [2].…”

Section: Introductionmentioning

confidence: 99%

Converse barrier certificate theorem

Wisniewski

Sloth

2013

52nd IEEE Conference on Decision and Control

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This paper presents a converse barrier certificate theorem for a generic dynamical system. We show that a barrier certificate exists for any safe dynamical system defined on a compact manifold.Other authors have developed a related result, by assuming that the dynamical system has no singular points in the considered subset of the state space. In this paper, we redefine the standard notion of safety to comply with generic dynamical systems with multiple singularities. Afterwards, we prove the converse barrier certificate theorem and illustrate the differences between ours and previous work by simple examples.

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Safety verification and reachability analysis for hybrid systems

Cited by 11 publications

References 18 publications

A machine learning approach for real-time reachability analysis

A machine learning approach for real-time reachability analysis

Real-Time Reachability for Verified Simplex Design

Converse barrier certificate theorem

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