Robust control of uncertain Markov Decision Processes with temporal logic specifications

Eric M. Wolff, Ufuk Topcu, Richard M. Murray
2012 2012 IEEE 51st IEEE Conference on Decision and Control (CDC)  
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
more » ... ing 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 -suboptimal robust control policy with time complexity O(log1 ) times that for the non-robust case. We then implement this control policy on the original dynamical system.
doi:10.1109/cdc.2012.6426174 dblp:conf/cdc/WolffTM12 fatcat:es3s4sunazekzi7cm2hdt3f7h4