Smoothing techniques-based distributed model predictive control algorithms for networks

Abstract

In this chapter we propose dual distributed methods based on smoothing techniques, called here the proximal center method and the interior-point Lagrangian method, to solve distributively separable convex problems. We also present an extension of these methods to the case of separable non-convex problems but with a convex objective function using a sequential convex programming framework. We prove that some relevant centralized model predictive control (MPC) problems for a network of coupling linear (non-linear) dynamical systems can be recast as separable convex (non-convex) problems for which our distributed methods can be applied. We also show that the solution of our distributed algorithms converges to the solution of the centralized problem and we provide estimates for the rate of convergence, which improve the estimates of some existing methods. © 2012 Springer-Verlag GmbH Berlin Heidelberg.