Structured preconditioning of conjugate gradients for path-graph network optimal control problems

Abstract

A structured preconditioned conjugate gradient (PCG) based linear system solver is developed for implementing Newton updates in second-order methods for a class of con- strained network optimal control problems. Of specific interest are problems with discrete-time dynamics arising from the path-graph interconnection of N heterogeneous sub-systems. The arithmetic complexity of each PCG step is O(NT), where T is the length of the time horizon. The proposed preconditioning involves a fixed number of block Jacobi iterations per PCG step. A decreasing analytic bound on the effective conditioning is given in terms of this number. The computations are decomposable across the spatial and temporal di..