Heuristic Search for Linear Positive Systems

This work considers infinite-horizon optimal control of positive linear systems applied to the case of network routing problems. We demonstrate the equivalence between Stochastic Shortest Path (SSP) problems and optimal control of a certain class of linear systems. This is used to construct a heuristic search framework for this class of linear systems inspired by existing methods for SSP. We propose a heuristics-based algorithm for finding local solutions to the analyzed class of optimal control problems with positive state and linear dynamics. More fundamentally, the results allow for analysis of the conditions for explicit solutions to the Bellman equation utilized by heuristic search methods.