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# Robust Control of Uncertain Markov Decision Processes with Temporal Logic Specifications

Wolff, Eric M. and Topcu, Ufuk and Murray, Richard M. (2011) Robust Control of Uncertain Markov Decision Processes with Temporal Logic Specifications. California Institute of Technology , USA. (Unpublished) http://resolver.caltech.edu/CaltechCDSTR:2011.008

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## Abstract

We present a method for designing robust controllers for dynamical systems with linear temporal logic specifications. We abstract the original system by a finite Markov Decision Process (MDP) that has transition probabilities in a specified uncertainty set. A robust control policy for the MDP is generated that maximizes the worst-case probability of satisfying the specification over all transition probabilities in the uncertainty set. To do this, we use a procedure from probabilistic model checking to combine the system model with an automaton representing the specification. This new MDP is then transformed into an equivalent form that satisfies assumptions for stochastic shortest path dynamic programming. A robust version of dynamic programming allows us to solve for a $\epsilon$-suboptimal robust control policy with time complexity $O(\log 1/\epsilon)$ times that for the non-robust case. We then implement this control policy on the original dynamical system.

Item Type: Report or Paper (Technical Report) The authors would like to thank Scott Livingston for helpful comments. This work was supported by an NSF Graduate Research Fellowship and the Boeing Corporation. Control and Dynamical Systems Technical Reports Temporal logic; Markov decision processes; robotics; robust control CaltechCDSTR:2011.008 http://resolver.caltech.edu/CaltechCDSTR:2011.008 You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format. 28147 CaltechCDSTR Imported from CaltechCDSTR 26 Sep 2011 26 Dec 2012 14:31

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