scholarly journals Efficient nonlinear filtering of a singularly perturbed stochastic hybrid system

2011 ◽  
Vol 14 ◽  
pp. 254-270 ◽  
Author(s):  
Jun H. Park ◽  
Boris Rozovskii ◽  
Richard B. Sowers
Keyword(s):  
State Estimation ◽  
Hybrid Systems ◽  
Hybrid System ◽  
Nonlinear Filtering ◽  
Efficient Estimation ◽  
Singularly Perturbed ◽  
Stochastic Hybrid Systems ◽  
Stochastic Hybrid System ◽  
Estimation Scheme ◽  
On Line

AbstractOur focus in this work is to investigate an efficient state estimation scheme for a singularly perturbed stochastic hybrid system. As stochastic hybrid systems have been used recently in diverse areas, the importance of correct and efficient estimation of such systems cannot be overemphasized. The framework of nonlinear filtering provides a suitable ground for on-line estimation. With the help of intrinsic multiscale properties of a system, we obtain an efficient estimation scheme for a stochastic hybrid system.

scholarly journals Verifying Stochastic Hybrid Systems with Temporal Logic Specifications via Model Reduction

2021 ◽  
Vol 20 (6) ◽  
pp. 1-27
Author(s):  
Yu Wang ◽  
Nima Roohi ◽  
Matthew West ◽  
Mahesh Viswanathan ◽  
Geir E. Dullerud
Keyword(s):  
Markov Chain ◽  
Hybrid Systems ◽  
Temporal Logic ◽  
Hybrid System ◽  
Original System ◽  
Stochastic Hybrid Systems ◽  
Statistical Model Checking ◽  
Stochastic Hybrid System ◽  
Finite State

We present a scalable methodology to verify stochastic hybrid systems for inequality linear temporal logic (iLTL) or inequality metric interval temporal logic (iMITL). Using the Mori–Zwanzig reduction method, we construct a finite-state Markov chain reduction of a given stochastic hybrid system and prove that this reduced Markov chain is approximately equivalent to the original system in a distributional sense. Approximate equivalence of the stochastic hybrid system and its Markov chain reduction means that analyzing the Markov chain with respect to a suitably strengthened property allows us to conclude whether the original stochastic hybrid system meets its temporal logic specifications. Based on this, we propose the first statistical model checking algorithms to verify stochastic hybrid systems against correctness properties, expressed in iLTL or iMITL. The scalability of the proposed algorithms is demonstrated by a case study.

scholarly journals Counterexample-Guided Abstraction-Refinement for Hybrid Systems Diagnosability Analysis

10.29007/t8n3 ◽  
2018 ◽  
Author(s):  
Hadi Zaatiti ◽  
Lina Ye ◽  
Philippe Dague ◽  
Jean-Pierre Gallois
Keyword(s):  
Hybrid Systems ◽  
Hybrid System ◽  
Timed Automata ◽  
Discrete Event ◽  
Fault Detection And Isolation ◽  
Time Constraints ◽  
Design Stage ◽  
Qualitative Level ◽  
On Line ◽  
Spurious Effect

Verifying behavioral or safety properties of hybrid systems, either at design stage such as state reachability and diagnosability, or on-line such as fault detection and isolation is a challenging task. We are concerned here with abstractions oriented towards hybrid systems diagnosability checking. The verification can be done on the abstraction by classical methods developed for discrete event systems extended with time constraints, which provide a counterexample in case of non-diagnosability. The absence of such a counterexample proves the diagnosability of the original hybrid system. In the presence of a counterexample, the first step is to check if it is not a spurious effect of the abstraction and actually exists for the hybrid system, witnessing thus non-diagnosability. Otherwise, we show how to refine the abstraction, guided by the elimination of the counterexample, and continue the process of looking for another counterexample until either a final result is obtained or we reach an inconclusive verdict. We make use of qualitative modeling and reasoning to compute discrete abstractions. Abstractions as timed automata are particularly studied as they allow one to handle time constraints that can be captured at a qualitative level from the hybrid system.

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