An algorithmic approach to stability verification of polyhedral switched systems

Prabhakar, Pavithra; Soto, Miriam García

doi:10.1109/acc.2014.6859056

Cited by 9 publications

(4 citation statements)

References 12 publications

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“…The hybridization procedure is implemented in Averist [15]. Averist is a stability verification tool based on quantitative predicate abstraction.…”

Section: Resultsmentioning

confidence: 99%

“…To overcome the difficulties with the template based search, an alternate approach based on abstraction-refinement was proposed by the authors in their previous work [14,15] for stability analysis of hybrid systems with piecewise constant and polyhedral inclusion dynamics. Here, a quantitative predicate abstraction (QPA) for stability analysis was presented, which extends the standard finite state graph construction of predicate abstraction [7], by annotating the edges with weights which capture information about the distance of the state to the equilibrium point during evolution along a trajectory.…”

Section: Introductionmentioning

confidence: 99%

“…This is a challenging problem, especially, when the number of edge switchings is not bounded. Hence, we propose to abstract the linear hybrid system to a polyhedral hybrid system for which the edge relation and weights can be efficiently computed (even in the presence of unbounded number of mode switches [15]).…”

Section: Introductionmentioning

confidence: 99%

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Hybridization for Stability Analysis of Switched Linear Systems

Prabhakar

Soto

2016

Proceedings of the 19th International Conference on Hybrid Systems: Computation and Control

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In this paper, we present a hybridization method for stability analysis of switched linear hybrid system (LHS), that constructs a switched system with polyhedral inclusion dynamics (PHS) using a state-space partition that is specific to stability analysis. We use a previous result based on quantitative predicate abstraction to analyse the stability of PHS. We show completeness of the hybridization based verification technique for the class of asymptotically stable linear system and a subclass of switched linear systems whose dynamics are pairwise Lipschitz continuous on the state-space and uniformly converging in time. For this class of systems, we show that by increasing the granularity of the region partition, we eventually reach an abstract switched system with polyhedral inclusion dynamics that is asymptotically stable. On the practical side, we implemented our approach in the tool Averist, and experimentally compared our approach with a state-of-the-art tool for stability analysis of hybrid systems based on Lyapunov functions. Our experimental results illustrate that our method is less prone to numerical errors and scales better than the traditional approaches. In addition, our tool returns a counterexample in the event that it fails to prove stability, providing feedback regarding the potential reason for instability. We also examined heuristics for the choice of state-space partition during refinement.

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“…The hybridization procedure is implemented in Averist [15]. Averist is a stability verification tool based on quantitative predicate abstraction.…”

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Hybridization for Stability Analysis of Switched Linear Systems

Prabhakar

Soto

2016

Proceedings of the 19th International Conference on Hybrid Systems: Computation and Control

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“…In practice, to succeed in proving stability, we may need to prune the graph to remove redundant information. For instance, [9,10] consider only the facets of the regions of the partition as nodes.…”

Section: Quantitative Predicate Abstraction (Qpa)mentioning

confidence: 99%

An Algorithmic Approach to Stability Verification of Hybrid Systems: A Summary

Prabhakar¹,

Soto²

EPiC Series in Computing

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This paper summarizes results related to a novel algorithmic approach for verifying stability of hybrid systems. The traditional approach based on Lyapunov function search suffers from several disadvantages -it relies on the user expertise to obtain good templates for the Lyapunov function; further, an unsuccessful attempt at instantiating the templates provides no insights into the choice of better templates. To overcome these difficulties, the algorithmic approach relies on an abstraction refinement framework which systematically searches for a proof and provides insights to the user in the event of a failure to prove stability. We summarize the new foundations, techniques and software tools that we have developed for the algorithmic approach to stability verification.

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Counterexample Guided Abstraction Refinement for Stability Analysis

Prabhakar

Soto

2016

Computer Aided Verification

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An algorithmic approach to stability verification of polyhedral switched systems

Cited by 9 publications

References 12 publications

Hybridization for Stability Analysis of Switched Linear Systems

Hybridization for Stability Analysis of Switched Linear Systems

An Algorithmic Approach to Stability Verification of Hybrid Systems: A Summary

Counterexample Guided Abstraction Refinement for Stability Analysis

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