Optimal control computation for cascade systems by structured Jacobi iterations

Abstract

A computational method is proposed for solving a structured finite-horizon optimal control problem. Specifically, a linear quadratic problem with discrete-time dynamics arising from a cascaded interconnection of N heterogeneous sub-systems is considered. This optimization problem is first formulated as a structured quadratic program whose size grows with extension of the time horizon T and/or cascade length N. An algorithm based on block Jacobi iterations is developed for solving the linear system of equations arising from the Karush-Kuhn-Tucker conditions for optimality. It is shown that the per-iteration complexity of the approach scales linearly in both TV and T. Moreover, the computation..