Obtaining the Most Likely Path in Stochastic Hidden Input Automata by Using Limited Optimal Discrete Control

Abstract

We propose a new modeling framework to compute the most likely path for stochastic hidden systems; where the computation is based on the control theory of discrete event systems. The main innovation in this proposed model is calculating which event will have a higher probability of occurring in the future by applying k-step to the likelihood of events occurring at discrete times, which will give us the best way to transition between situations. We encode the problem as a node built with synchronous data-flow equations; then we apply the synthesis algorithm to the node in order to generate a controller that will find the most likely state sequence; where the algorithm is limited to a sliding window of a fixed number of discrete steps. We experimentally evaluate and validate our approach by comparing it with several algorithms, which are the most common and suitable algorithms applied for the best path calculation.

Keywords

• Baum-Welch algorithm
• discrete controller synthesis
• hidden systems
• optimal control
• Viterbi algorithm