Analytical Framework for Hybrid Systems Using Discrete-Time Markov Chain Approaches
DOI:
https://doi.org/10.64137/XXXXXXXX/IJMAR-V1I1P103Keywords:
Hybrid systems, Discrete-time markov chain, Probabilistic model checking, Cyber-physical systems, State-space partitioning, PCTL, System reliabilityAbstract
Continuous or discrete dynamics with their interaction have been called hybrid systems and are ubiquitous in the design of many complex systems today, including cyber-physical systems, automated control systems and real-time embedded systems. The twofold nature of such state evolution presents these systems with peculiar problems of verification, control, and analysis. Also in this paper, I present an analytical model that uses the Discrete-Time Markov Chains (DTMCs) to model, analyze and predict the behaviour of the hybrid systems. DTMCs offer a probabilistic modeling framework which is capable of describing the stochastic dynamics of discrete hybrids efficiently and in a very elegant manner. The framework suggests a new approach to discretizing the ongoing dynamics and incorporating them in a DTMC-based analysis framework. The suggested approach is building transition probability matrices, a probabilistic state-space description and verification with the help of model checking techniques. The framework also uses a method of partitioning the continuous state space, resulting in abstract states which become an input to the DTMC model. The relevance of the framework is proved, inter alia, by several case studies of building temperature control systems, robotic navigation, and fault detection of automated systems. The results of the simulation depict the high level of accuracy and efficiency of the simulations compared to the traditional methods of hybrid system solvers. The key contributions of the paper can be listed as the follows: (1) A generalization of DTMC-based modeling strategy to hybrid systems, (2) A probabilistic abstraction approach to continuous systems, (3) Probabilistic verification approaches using PCTL (Probabilistic Computation Tree Logic), and (4) A case study evaluation. The paper is a contribution towards the reconciliation of deterministic modeling of hybrid systems with probabilistic verification methods and is of use when put to practice by engineers and researchers working in the field of reliability and performance analysis of systems
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