2014/07/10 by Majid Zamani, Alessandro Abate, Zamani, Majid +3 · 1 citation
Computer Science · Engineering · #Control and Stability of Dynamical Systems #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #Formal Methods in Verification #Logic in Computer Science (cs.LO) #Optimization and Control (math.OC) #Petri Nets in System Modeling #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · doi:10.48550/arxiv.1407.2730
openalex publication_date 2014/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Stochastic switched systems are a relevant class of stochastic hybrid systems with probabilistic evolution over a continuous domain and control-dependent discrete dynamics over a finite set of modes. In the past few years several different techniques have been developed to assist in the stability analysis of stochastic switched systems. However, more complex and challenging objectives related to the verification of and the controller synthesis for logic specifications have not been formally investigated for this class of systems as of yet. With logic specifications we mean properties expressed as formulae in linear temporal logic or as automata on infinite strings. This paper addresses these complex objectives by constructively deriving approximately equivalent (bisimilar) symbolic models of stochastic switched systems. More precisely, this paper provides two different symbolic abstraction techniques: one requires state space discretization, but the other one does not require any space discretization which can be potentially more efficient than the first one when dealing with higher dimensional stochastic switched systems. Both techniques provide finite symbolic models that are approximately bisimilar to stochastic switched systems under some stability assumptions on the concrete model. This allows formally synthesizing controllers (switching signals) that are valid for the concrete system over the finite symbolic model, by means of mature automata-theoretic techniques in the literature. The effectiveness of the results are illustrated by synthesizing switching signals enforcing logic specifications for two case studies including temperature control of a six-room building.