Poster Abstract: Decoding Output Sequences for Discrete-Time Linear Hybrid Systems.

This paper studies the decoding problem of discrete-time stochastic hybrid systems with linear dynamics at each mode. The problem of reconstructing the sequence of continuous states, modes, and transitions of a hybrid system given only a sequence of possibly noisy outputs is referred to as the decoding problem 1. The decoding problem is NP-complete [4] and can be reduced to solving a mixed integer linear program (MILP). In this paper, we propose a solution that solves a relaxation of the decoding problem. The approach iterates over two steps - (a) fixing the sequence of modes and transitions for the given output sequence; and (b) estimating the continuous states. To make the first part tractable, we identify a finite subset of mode/transition sequences that “covers” the set of all such possible sequences and then iterate over this subset instead. The cover is generated using randomized algorithms and justified using well-known probabilistic arguments with high confidence. We demonstrate the proposed approach on a set of seven benchmarks. We observe that a relatively tiny subset of all possible mode/transition sequences suffices as a cover and the proposed approach solves the resulting state estimation problem rapidly by utilizing a tree data structure.