Distributed Solution of Constrained Optimal Control Problems Using the Alternating Direction Method of Multipliers

Many control problems in science and engineering can be formulated as optimal control problems (OCP) such as load changes in process control or point-to-point motion of industrial robots in a time-optimal or energy-optimal way while accounting for physical or security constraints. Hence, an efficient way to handle constrained OCPs is an important topic of research. A promising approach to address this issue is a transformation technique allowing to reformulate an inequality constrained OCP into an equality constrained counterpart. The reformulated OCP reveals to possess a particular structure that is favorable for a decomposition and the application of distributed optimization methods. Motivated by the Augmented Lagrangian approach, the structure of the reformulated OCP can be exploited to derive a decomposition method for splitting up the entire OCP into smaller subproblems. In addition, an algorithm is presented that follows the ideas of the Alternating Direction Method of Multipliers (ADMM) and solves the resulting subproblems in a distributed manner. The approach is applied to a mechatronic example system to demonstrate the performance of the presented method. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)