On computing quadratic controls for acyclic networks of heterogeneous systems

In this paper we consider the problem of computing finite-horizon quadratic optimal controls for a network of interconnected heterogeneous linear systems. We assume that the network is isomorphic to an acyclic directed graph and propose a solution to the problem via dynamic programming. This yields a finite sequence of smaller problems to be solved. Each smaller problem is associated with a node (or collection of such) in the network graph. It involves only local information and information from neighbours. As such, the solution algorithm lends itself to a distributed implementation. We numerically compare the performance of the proposed solution with computing the finite-horizon optimal controls by solving the global problem without exploiting structure.