Improved Dual Decomposition for Distributed Model Predictive Control ⋆

In dual decomposition, the dual to an optimization problem with a specific structure is solved in distributed fashion using (sub)gradient and recently also fast gradient methods. The traditional dual decomposition suffers from two main short-comings. The first is that the convergence is often slow, although fast gradient methods have significantly improved the situation. The second is that computation of the optimal step-size requires centralized computations, which hinders a fully distributed implementation of the algorithm. In this paper, the first issue is addressed by providing a tighter quadratic approximation of the dual function than what has previously been reported in the literature. Then a distributed algorithm is presented in which the provided dual function approximation is minimized in each step. Since the approximation is more accurate than the approximation used in standard and fast dual decomposition, the convergence properties are improved. For the second issue, we extend a recent result to allow for a fully distributed parameter selection in the algorithm. Further, we show how to apply the algorithm to optimization problems arising in distributed model predictive control (DMPC) and that the proposed algorithm enjoys distributed reconfiguration, i.e. plug-and-play, in the DMPC context.