Dynamic Reduction of The Iterations Requirement in A Distributed Model Predictive Control

In this paper, we propose to reduce the number of iterations required in the implementation of distributed Model Predictive Control (dMPC) based on dual decomposition. To this aim, a dynamic Lagrange multipliers fixation algorithm (DLMFA) is proposed by continually fixing the value of Lagrange multipliers, and a local optimization problems dynamic sizing algorithm (LOPDSA) is proposed by continually reducing the size of local optimization problem during the iteration through an original prediction horizon reduction. The proposed algorithms are based on the Uzawa method, which is improved because of the specific nature of the constraints in a MPC context. The basics of these improvements stem from the particular behavior of the Lagrange multipliers and their fluctuations over the prediction horizon. Numerical experiments have shown that the iteration number, as well as the computation time of LOPDSA, are significantly reduced compared to Uzawa method.