Computational techniques for the verification of hybrid systems

Tomlin, Claire J.; Mitchell, Ian M.; Bayen, Alexandre M.; Oishi, Meeko

doi:10.1109/jproc.2003.814621

Cited by 309 publications

(208 citation statements)

References 66 publications

Supporting

Mentioning

207

Contrasting

Order By: Relevance

“…The most popular of such techniques rely either upon the linearity of the distinct subsystems of the hybrid system under investigation [10], [21], the Hamilton-Jacobi-Bellman Equation [22], or Lyapunov-type analysis [14], [17], [18]. Though the Hamilton-Jacobi-Bellman based methods work even in the presence of general nonlinear dynamics, they rely upon statespace discretization which can restrict their applicability to systems of low dimensionality.…”

Section: Introductionmentioning

confidence: 99%

Convex computation of the reachable set for controlled polynomial hybrid systems

Shia

Vasudevan

Bajcsy

et al. 2014

53rd IEEE Conference on Decision and Control

View full text Add to dashboard Cite

Abstract-This paper presents an approach to computing the time-limited backwards reachable set (BRS) of a semialgebraic target set for controlled polynomial hybrid systems with semialgebraic state and input constraints. By relying on the notion of occupation measures, the computation of the BRS of a target set that may be distributed across distinct subsystems of the hybrid system, is posed as an infinite dimensional linear program (LP). Computationally tractable approximations to this LP are constructed via a sequence of semidefinite programs each of which is proven to construct an outer approximation of the true BRS with asymptotically vanishing conservatism. In contrast to traditional Lyapunov based approaches, the presented approach is convex and does not require any form of initialization. The performance of the presented algorithm is illustrated on 2 nonlinear controlled hybrid systems.

show abstract

Section: Introductionmentioning

confidence: 99%

Convex computation of the reachable set for controlled polynomial hybrid systems

Shia

Vasudevan

Bajcsy

et al. 2014

53rd IEEE Conference on Decision and Control

View full text Add to dashboard Cite

show abstract

“…In another vein, several other techniques have also been developed for approximate reachability analysis. Such techniques rely on numerical methods for solving the Hamilton Jacobi equations [23], ellipsoidal calculus [13,6], flow-pipe approximations [9], and polygonal approximations [5,4,2].…”

Section: Introductionmentioning

confidence: 99%

Safety Verification of Hybrid Systems Using Barrier Certificates

Prajna

Jadbabaie

2004

Lecture Notes in Computer Science

507

486

View full text Add to dashboard Cite

Abstract. This paper presents a novel methodology for safety verification of hybrid systems. For proving that all trajectories of a hybrid system do not enter an unsafe region, the proposed method uses a function of state termed a barrier certificate. The zero level set of a barrier certificate separates the unsafe region from all possible trajectories starting from a given set of initial conditions, hence providing an exact proof of system safety. No explicit computation of reachable sets is required in the construction of barrier certificates, which makes nonlinearity, uncertainty, and constraints can be handled directly within this framework. The method is also computationally tractable, since barrier certificates can be constructed using the sum of squares decomposition and semidefinite programming. Some examples are provided to illustrate the use of the method.

show abstract

“…There has been a wealth of research on safety control for hybrid systems in which the state is known [5,25,26,37,39,[48][49][50]. In [39,[48][49][50], the safety control problem is elegantly formulated in the context of optimal control and leads to R. Verma is with the Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI, 48109 USA.…”

Section: Introductionmentioning

confidence: 99%

“…In [39,[48][49][50], the safety control problem is elegantly formulated in the context of optimal control and leads to R. Verma is with the Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI, 48109 USA. e-mail: rajverma@umich.edu.…”

Section: Introductionmentioning

confidence: 99%

“…This equation implicitly determines the maximal controlled invariant set and the least restrictive feedback control map. Due to the complexity of exactly solving the HJB equation, researchers have been investigating approximate algorithms for computing inner-approximations of the maximal controlled invariant set [30,31,44,50]. Termination of the algorithm that computes the maximal controlled invariant set is often an issue and work has been investigating special classes of systems that allow to prove termination [46][47][48].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Safety Control of Hidden Mode Hybrid Systems

Verma

Vecchio

2012

IEEE Trans. Automat. Contr.

View full text Add to dashboard Cite

Abstract-In this paper, we consider the safety control problem for Hidden Mode Hybrid Systems (HMHSs), which are a special class of hybrid automata in which the mode is not available for control. For these systems, safety control is a problem with imperfect state information. We tackle this problem by introducing the notion of non-deterministic discrete information state and by translating the problem to one with perfect state information. The perfect state information control problem is obtained by constructing a new hybrid automaton, whose discrete state is an estimate of the HMHS mode and is, as such, available for control. This problem is solved by computing the capture set and the least restrictive control map for the new hybrid automaton. Sufficient conditions for the termination of the algorithm that computes the capture set are provided. Finally, we show that the solved perfect state information control problem is equivalent to the original problem with imperfect state information under suitable assumptions. We illustrate the application of the proposed technique to a collision avoidance problem between an autonomous vehicle and a human driven vehicle at a traffic intersection.Index Terms-Mode estimation, dynamic feedback, multiagent systems.

show abstract

Computational techniques for the verification of hybrid systems

Abstract: Hybrid system theory lies at the intersection of the fields of engi-

Cited by 309 publications

References 66 publications

Convex computation of the reachable set for controlled polynomial hybrid systems

Convex computation of the reachable set for controlled polynomial hybrid systems

Safety Verification of Hybrid Systems Using Barrier Certificates

Safety Control of Hidden Mode Hybrid Systems

Contact Info

Product

Resources

About