A Hybrid Bounding Method for Computing an Over-Approximation for the Reachable Set of Uncertain Nonlinear Systems

Abstract. This paper presents a bounded model checking (BMC) tool called hydlogic for hybrid systems. It translates a reachability problem of a nonlinear hybrid system into a predicate logic formula involving arithmetic constraints, and checks the satisfiability of the formula based on a satisfiability modulo theories (SMT) method. We tightly integrate (i) an incremental SAT solver to enumerate the possible sets of constraints and (ii) an interval-based solver for hybrid constraint systems (HCSs) to solve the constraints described in the formulas. The HCS solver verifies the occurrence of a discrete change by enclosing continuous states that may cause the discrete change by a set of boxes. We adopt the existence property of a unique solution in the boxes computed by the HCS solver as (i) a proof of the reachability of a model, and (ii) a guide in the over-approximation refinement procedure. Our hydlogic implementation successfully handled several examples including those with nonlinear constraints.

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“…The refinement method can be improved in several ways using techniques for handling nonlinear ODEs with uncertainties [14], for example.…”

Section: Resultsmentioning

confidence: 99%

An interval-based SAT modulo ODE solver for model checking nonlinear hybrid systems

Ishii

Ueda

Hosobe

2011

Int J Softw Tools Technol Transfer

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“…As indicated in (Ramdani et al, 2009), The method of hybrid bounding is an approach of reachability analysis. It allows thus to find the envelope enclosing all possible trajectories of the robot in order to study its stability.…”

Section: Principle Of the Hybrid Bounding Methodsmentioning

confidence: 99%

“…As mentioned in (Ramdani et al, 2009), a hybrid automaton used to find the envelope which frames, in a guaranteed way, the real robot's path, is generally considered as being one 6-uplet H = (Q, X, P, F, T, RI) defined by:…”

Section: Hybrid Automaton For the Robot's Controlmentioning

confidence: 99%

“…Toibero and Kuchen, 2007). Among these approaches, we adopt the reachability analysis using the interval analysis (Ramdani et al, 2009). This approach, based on a hybrid automatons, allows finding all the minimal and maximal trajectories of the system, governed by Ordinary Differential Equations (ODE), and to check according to these later if the unwanted system configuration could occurs.…”

Section: Introductionmentioning

confidence: 99%

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Hybrid and Multi-controller Architecture for Autonomous System - Application to the Navigation of a Mobile Robot

Azzabi

Regaieg

Adouane

et al. 2014

Proceedings of the 11th International Conference on Informatics in Control, Automation and Robotics

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Abstract:This paper deals with the problem of unicycle mobile robot navigation in cluttered environments. It presents in particular an approach which permits to verify the stability of the control architecture of mobile robot using the reachability analysis. To perform this analysis, we consider the robot as a hybrid dynamic system. The latter is modeled by an hybrid automata in order to verify the reachability property by using the interval analysis.The simulation results validate the proposed control architecture.

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“…A potentially interesting future transformation pass could be implemented in HyST to convert continuous systems with uncertainty into hybrid systems in which there is no uncertainty in the continuous dynamics, e.g. following the work of Ramdani et al [32].…”

Section: Discussionmentioning

confidence: 99%

Non-linear Continuous Systems for Safety Verification

Sogokon¹,

Ghorbal²,

Johnson³

EPiC Series in Computing

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Safety verification of hybrid dynamical systems relies crucially on the ability to reason about reachable sets of continuous systems whose evolution is governed by a system of ordinary differential equations (ODEs). Verification tools are often restricted to handling a particular class of continuous systems, such as e.g. differential equations with constant right-hand sides, or systems of affine ODEs. More recently, verification tools capable of working with non-linear differential equations have been developed. The behavior of non-linear systems is known to be in general extremely difficult to analyze because solutions are rarely available in closed-form. In order to assess the practical utility of the various verification tools working with non-linear ODEs it is very useful to maintain a set of verification problems. Similar efforts have been successful in other communities, such as automated theorem proving, SAT solving and numerical analysis, and have accelerated improvements in the tools and their underlying algorithms. We present a set of 65 safety verification problems featuring non-linear polynomial ODEs and for which we have proofs of safety. We discuss the various issues associated with benchmarking the currently available verification tools using these problems.

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A Hybrid Bounding Method for Computing an Over-Approximation for the Reachable Set of Uncertain Nonlinear Systems

Cited by 81 publications

References 24 publications

An interval-based SAT modulo ODE solver for model checking nonlinear hybrid systems

An interval-based SAT modulo ODE solver for model checking nonlinear hybrid systems

Hybrid and Multi-controller Architecture for Autonomous System - Application to the Navigation of a Mobile Robot

Non-linear Continuous Systems for Safety Verification

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