Linear quadratic control computation for systems with a directed tree structure

Abstract

A computational method is proposed for solving a structured quadratic optimal control problem subject to linear discrete-time dynamics arising from a directed tree structured interconnection of heterogeneous sub-systems. The problem is first formulated as a quadratic program with structure along three dimensions of the decision space. A nested algorithm based on block Jacobi iterations is proposed for the linear system of equations obtained from the corresponding first-order optimality conditions. It is shown that the per iteration computational burden scales favorably with increasing problem size in each dimension. The computations at each iteration are amenable to distributed implementatio..