Computation time analysis of a distributed optimization algorithm applied to automated irrigation networks

This paper considers the computation time of two algorithms for solving a structured constrained linear optimal control problem with finite horizon quadratic cost within the context of automated irrigation networks. The first is a standard centralized algorithm based on the interior point method that does not exploit problem structure. The second is distributed and based on a consensus algorithm, not specifically tailored to account for system structure, but devised rather to facilitate the management of conflicting computational and communication overheads. It is shown that there is a significant advantage in terms of computation time in using the second algorithm in large-scale networks. Specifically, for a fixed horizon length the computation time of the centralized algorithm grows as O(n⁴) with the number n of sub-systems. By contrast, it is observed via a combination of analysis and experiment that the computation time of the distributed algorithm grows as O(n) with the number n of sub-systems.