Structured Preconditioning of Conjugate Gradients for Path-Graph Network Optimal Control Problems

• 成果类型: Article
• 署名作者: Zafar, Armaghan; Cantoni, Michael; Farokhi, Farhad
• 署名单位: University of Melbourne
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3107246
• 发表日期: 2022
• 页码: 4115-4122
• 关键词: Optimal control of networks; structured secondorder solver; system chains

摘要

A structured preconditioned conjugate gradient (PCG) based solver is developed for implementing the Newton updates in second-order methods for a class of constrained network optimal control problems. Of specific interest are problems with discrete-time dynamics arising from the path-graph interconnection of N heterogeneous subsystems. 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 associated computations are decomposable across the spatial and temporal dimensions of the optimal control problem, into subproblems of size independent of N and T. Numerical results are provided for two example systems.