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Nejati, Ameneh; Zamani, Majid (2020): Compositional Construction of Finite MDPs for Continuous-Time Stochastic Systems: A Dissipativity Approach. In: Ifac Papersonline, Vol. 53, No. 2: pp. 1962-1967
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This paper provides a compositional scheme based on dissipativity approaches for constructing finite abstractions of continuous-time continuous-space stochastic control systems. The proposed framework enjoys the structure of the interconnection topology and employs a notion of stochastic storage functions, that describe joint dissipativity-type properties of subsystems and their abstractions. By utilizing those stochastic storage functions, one can establish a relation between continuous-time continuous-space stochastic systems and their finite counterparts while quantifying probabilistic distances between their output trajectories. Consequently, one can employ the finite system as a suitable substitution of the continuous-time one in the controller design process with a guaranteed error bound. In this respect, we first leverage dissipativity-type compositional conditions for the compositional quantification of the distance between the interconnection of continuous-time continuous-space stochastic systems and that of their discrete-time (finite or infinite) abstractions. We then consider a specific class of stochastic affine systems and construct their finite abstractions together with their corresponding stochastic storage functions. We illustrate the effectiveness of the proposed techniques by applying them to a physical case study. Copyright (C) 2020 The Authors.