Reach Set Computations Using Real Quantifier Elimination

Anai, Hirokazu; Weispfenning, Volker

doi:10.1007/3-540-45351-2_9

Cited by 74 publications

(48 citation statements)

References 19 publications

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“…In addition to linear and piecewise linear/affine systems (on which the computational methods proposed in this paper mostly apply), quantifier elimination methods can also be applied to a considerably more general class of discrete-time systems, for example systems whose dynamics and constraints are encoded by piecewise polynomial functions. The limits of the applicability of this approach to continuous-time systems are investigated in [23], where methods for using systems amenable to the quantifier elimination approach to approximate even more general classes of systems are also discussed.…”

Section: )mentioning

confidence: 99%

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Reachability Analysis of Discrete-Time Systems With Disturbances

Raković

Kerrigan

Mayne

et al. 2006

IEEE Trans. Automat. Contr.

156

108

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Abstract-This paper presents new results that allow one to compute the set of states that can be robustly steered in a finite number of steps, via state feedback control, to a given target set. The assumptions that are made in this paper are that the system is discrete-time, nonlinear and time-invariant and subject to mixed constraints on the state and input. A persistent disturbance, dependent on the current state and input, acts on the system. Existing results are not able to address state-and input-dependent disturbances and the results in this paper are, therefore, a generalization of previously published results. One of the key aims of this paper is to present results such that one can perform the relevant set computations using polyhedral algebra and computational geometry software, provided the system is piecewise affine and the constraints are polygonal. Existing methods are only applicable to piecewise affine systems that either have no control inputs or no disturbances, whereas the results in this paper remove this limitation. Some simple examples are also given that show that, even if all the relevant sets are convex and the system is linear, convexity of the set of controllable states cannot be guaranteed.

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Section: )mentioning

confidence: 99%

“…, the set of states that are robustly controllable to in one step, is given by (23) where is given by (24) Proof: A graphical interpretation of the proof is given in Fig. 1.…”

Section: Theorem 1 (Predecessor Set)mentioning

confidence: 99%

Reachability Analysis of Discrete-Time Systems With Disturbances

Raković

Kerrigan

Mayne

et al. 2006

IEEE Trans. Automat. Contr.

156

108

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show abstract

“…systems with piecewise constant derivatives [1,3,10,33]), or in discrete dynamics (e.g. [5,40]). Based on these results, various verification tools have been implemented, such as Kronos [60] and Uppaal [41] for timed automata, HyTech [32] for linear hybrid automata 3 and Requiem [40] for hybrid systems where linear differential equations have special eigenstructure and discrete dynamics can only have memoryless resets.…”

Section: Hybrid Systems Analysis: a Brief Reviewmentioning

confidence: 99%

Hybridization methods for the analysis of nonlinear systems

2007

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In this article, we describe some recent results on the hybridization methods for the analysis of nonlinear systems. The main idea of our hybridization approach is to apply the hybrid systems methodology as a systematic approximation method. More concretely, we partition the state space of a complex system into regions that only intersect on their boundaries, and then approximate its dynamics in each region by a simpler one. Then, the resulting hybrid system, which we call a hybridization, is used to yield approximate analysis results for the original system. We also prove important properties of the hybridization, and propose two effective hybridization construction methods, which allow approximating the original nonlinear system with a good convergence rate.

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“…Several approaches [2,13,19,20] use quantifier elimination [8] in first-order real arithmetic for model checking hybrid automata. Thus, we use the same decision procedure as a basis for handling arithmetic of non-linear flows.…”

Section: Introductionmentioning

confidence: 99%

Differential Dynamic Logic for Verifying Parametric Hybrid Systems

Platzer

Lecture Notes in Computer Science

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Abstract. We introduce a first-order dynamic logic for reasoning about systems with discrete and continuous state transitions, and we present a sequent calculus for this logic. As a uniform model, our logic supports hybrid programs with discrete and differential actions. For handling real arithmetic during proofs, we lift quantifier elimination to dynamic logic. To obtain a modular combination, we use side deductions for verifying interacting dynamics. With this, our logic supports deductive verification of hybrid systems with symbolic parameters and first-order definable flows. Using our calculus, we prove a parametric inductive safety constraint for speed supervision in a train control system.

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Reach Set Computations Using Real Quantifier Elimination

Cited by 74 publications

References 19 publications

Reachability Analysis of Discrete-Time Systems With Disturbances

Reachability Analysis of Discrete-Time Systems With Disturbances

Hybridization methods for the analysis of nonlinear systems

Differential Dynamic Logic for Verifying Parametric Hybrid Systems

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