Approximate Completed Trace Equivalence of Three Dimensional t-Model Nonlinear Algebraic Hybrid Systems

Yang, Hao; Wu, Jinzhao; Zhang, Zhiwei; Liu, Yang

doi:10.12785/amis/070506

Cited by 1 publication

(4 citation statements)

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“…With some restrictions, a hybrid system can be specialized into an inhomogeneous linear algebraic hybrid system, which is ubiquitous in reality [4,5,24]. Definition 3 (Inhomogeneous linear algebraic hybrid system, ILAHS).…”

Section: Definition 2 (Trajectory)mentioning

confidence: 99%

“…A Special Case: The approaches proposed in papers [4,5,24] use the Frobenius norm to study approximate equivalence of real-time linear algebraic hybrid automaton. Their approaches can only apply to a class of special matrices.…”

Section: ε-Approximate Completed Trace Equivalence Of Ilahsmentioning

confidence: 99%

“…Functional equivalence simplifies the system by removing the duplicate branches. The papers by Glabbeek [2,3] proposed fourteen kinds of linear time-branching time equivalence relations, and the completed trace equivalence is a basic state-space equivalence relation, which can be used to further reduce the states of hybrid systems [4,5].…”

Section: Introductionmentioning

confidence: 99%

“…Our approximation technology is, however, to identify the approximate behavior equivalence among the hybrid systems. So far, there exist few papers focused on the approximation analysis of the ILAHS' behavior equivalence [4,5,24]. Unfortunately, their methods are based on Matrix Jordan Standard Type, which only apply to special cases and cannot deal with the infinite trajectory condition, whereas our method can solve this problem.…”

Section: Introductionmentioning

confidence: 99%

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Approximate Completed Trace Equivalence of ILAHSs Based on SAS Solving

Xiong

2019

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The ILAHS (inhomogeneous linear algebraic hybrid system) is a kind of classic hybrid system. For the purpose of optimizing the design of ILAHS, one important strategy is to introduce equivalence to reduce the states. Recent advances in the hybrid system indicate that approximate trace equivalence can further simplify the design of ILAHS. To address this issue, the paper first introduces the trajectory metric d t r j for measuring the deviation of two hybrid systems’ behaviors. Given a deviation ε ≥ 0 , the original ILAHS of H 1 can be transformed to the approximate ILAHS of H 2 , then in trace equivalence semantics, H 2 is further reduced to H 3 with the same functions, and hence H 1 is ε -approximate trace equivalent to H 3 . In particular, ε = 0 is a traditional trace equivalence. We implement an approach based on RealRootClassification to determine the approximation between the ILAHSs. The paper also shows that the existing approaches are only special cases of our method. Finally, we illustrate the effectiveness and practicality of our method on an example.

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Section: Definition 2 (Trajectory)mentioning

confidence: 99%

Section: ε-Approximate Completed Trace Equivalence Of Ilahsmentioning

confidence: 99%