Asynchronous ADMM for nonlinear continuous-time systems

This paper presents synchronous as well as asynchronous formulations of the alternating direction method of multipliers (ADMM) for solving continuous-time nonlinear distributed model predictive control (DMPC) problems. It is shown that the optimal control problems of certain system classes can be transformed to fit the consensus-based ADMM variant problem formulation. The arising subproblems are solved locally on the agent level while the consensus step is solved centrally by a coordinator. Furthermore, the convergence of the synchronous and asynchronous ADMM algorithms to their respective first-order optimality conditions is presented in a continuous-time setting. The algorithm is applied to different example systems for which the convergence behavior and influence of the individual algorithmic parameters are investigated. The computation time of the agents remains unaffected by the system size and thus demonstrates the applicability to high-scaled systems. Moreover, results show that the asynchronous algorithm performs better in terms of execution time when compared to its synchronous counterpart.