Approximate Markovian abstractions for linear stochastic systems

M. Lahijanian, S. B. Andersson, C. Belta
2012 2012 IEEE 51st IEEE Conference on Decision and Control (CDC)  
In this paper, we present a method to generate a finite Markovian abstraction for a discrete time linear stochastic system evolving in a full dimensional polytope. Our approach involves an adaptation of an existing approximate abstraction procedure combined with a bisimulation-like refinement algorithm. It proceeds by approximating the transition probabilities from one region to another by calculating the probability from a single representative point in the first region. We derive the exact
more » ... derive the exact bound of the approximation error and an explicit expression for its growth over time. To achieve a desired error value, we employ an adaptive refinement algorithm that takes advantage of the dynamics of the system. We demonstrate the performance of our method through simulations.
doi:10.1109/cdc.2012.6426184 dblp:conf/cdc/LahijanianAB12 fatcat:534u4ikrybdandf654bon2frpy