Distributed Model Predictive Control for a Class of Hybrid system based on Lagrangian Relaxation

In this paper, a distributed algorithm is proposed to solve a model predictive control problem for some continuous systems governed by discrete inputs. The first step is to rewrite the global problem, into a new optimization problem under constraints. Then the distributed structure can be obtained using Lagrangian relaxation. But, as the optimization variables are not continuous but discrete, the strong duality conditions are no longer ensured. The main contribution in this paper is to define a mechanism which overcomes this difficulty. The effectiveness of the proposed algorithm is illustrated with some academical simulations.