Abstraction of continuous control problems considered as MDPs

H. G. Tanner and A. Stager, Data-Driven Abstractions for Robots With Stochastic Dynamics, IEEE Transactions on Robotics, vol. 38, no. 3, pp. 1686-1702, June 2022 DOI: 10.1109/TRO.2021.3119209.

This article describes the construction of stochastic, data-based discrete abstractions for uncertain random processes continuous in time and space. Motivated by the fact that modeling processes often introduce errors which interfere with the implementation of control strategies, here the abstraction process proceeds in reverse: the methodology does not abstract models; rather it models abstractions. Specifically, it first formalizes a template for a family of stochastic abstractions, and then fits the parameters of that template to match the dynamics of the underlying process and ground the abstraction. The article also shows how the parameter-fitting approach can be implemented based on a probabilistic model validation approach which draws from randomized algorithms, and results in a discrete abstract model which is approximately simulated by the actual process physics, at a desired confidence level. In this way, the models afford the implementation of symbolic control plans with probabilistic guarantees at a desired level of fidelity.

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