Heuristic Search for Linear Positive Systems

Abstract

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 linear {positive} systems inspired by existing methods for SSP. {We propose a heuristics-based algorithm for {efficiently} finding local solutions to the analyzed class of optimal control problems with {a given initial} state and {positive} linear dynamics.} {By leveraging the bound on optimality in each state provided by the heuristics, we also derive a novel distributed algorithm for calculating local controllers within a specified performance bound, with a distributed condition for termination.} More fundamentally, the results allow for analysis of the conditions for explicit solutions to the Bellman equation utilized by heuristic search methods.