NLTOOLBOX: A Library for Reachability Computation of Nonlinear Dynamical Systems

Testylier, Romain; Dang, Thao

doi:10.1007/978-3-319-02444-8_37

Cited by 27 publications

(15 citation statements)

References 14 publications

(20 reference statements)

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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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“…The problem of finding an execution connecting two configurations can be undecidable depending on expressions used in assignments; nevertheless various techniques [19] can be tried, such as various types of model-checking, symbolic execution, and SMT solvers. For example abstract interpretation techniques are used in [20][21][22] for the reachability analysis of a model with variables and assignments and tools have been developed (CBMC [23], STG [24], NLToolBox [25], UPPAAL [26], etc.). These reachability analysis techniques and tools can be used for a single machine.…”

Section: Reachability In Emmtsmentioning

confidence: 99%

Reachability in hierarchical machines

Timo

Petrenko

Dury

et al. 2014

Proceedings of the 2014 IEEE 15th International Conference on Information Reuse and Integration (IEEE IRI 2014)

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In this paper we study the reachability analysis problem for timed systems specified in a hierarchical manner. First we provide a formal model, called hierarchical extended Mealy machine with timer, input and output events, as well with input, output and context variables. Then we present a synchronous semantics of the model. A main feature of this model is that the crossing of superstates' boundaries is forbidden, i.e., transitions between states in different superstates are not allowed. Finally we propose a reachability analysis method for finding (minimal) executions between configurations of a given deterministic hierarchical machine. Executions may require resetting of some constituent machines by entering some of their ancestor states. The algorithm exploits the hierarchical structure of the machine. The complexity of our algorithm is linear in R where R is the complexity of the reachability analysis of constituent machines.

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“…Outer-approximations have been dealt with ellipsoidal [20], sub-polyhedral techniques, such as zonotopes or support functions, and Taylor model based methods, for both linear and nonlinear systems [2,[4][5][6]10,14,17,26]. A number of corresponding implementations exist [1,3,7,13,22,25,29]. Much less methods have been proposed, that answer the more difficult problem of inner-approximation.…”

Section: Introductionmentioning

confidence: 99%

Inner and Outer Approximating Flowpipes for Delay Differential Equations

Goubault¹,

Putot²,

Sahlmann³

2018

Computer Aided Verification

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Delay differential equations are fundamental for modeling networked control systems where the underlying network induces delay for retrieving values from sensors or delivering orders to actuators. They are notoriously difficult to integrate as these are actually functional equations, the initial state being a function. We propose a scheme to compute inner and outer-approximating flowpipes for such equations with uncertain initial states and parameters. Inner-approximating flowpipes are guaranteed to contain only reachable states, while outer-approximating flowpipes enclose all reachable states. We also introduce a notion of robust inner-approximation, which we believe opens promising perspectives for verification, beyond property falsification. The efficiency of our approach relies on the combination of Taylor models in time, with an abstraction or parameterization in space based on affine forms, or zonotopes. It also relies on an extension of the mean-value theorem, which allows us to deduce inner-approximating flowpipes, from flowpipes outerapproximating the solution of the DDE and its Jacobian with respect to constant but uncertain parameters and initial conditions. We present some experimental results obtained with our C++ implementation.

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NLTOOLBOX: A Library for Reachability Computation of Nonlinear Dynamical Systems

Cited by 27 publications

References 14 publications

A machine learning approach for real-time reachability analysis

A machine learning approach for real-time reachability analysis

Reachability in hierarchical machines

Inner and Outer Approximating Flowpipes for Delay Differential Equations

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