An ADMM-based algorithm for stabilizing distributed model predictive control without terminal cost and constraint

Abstract

The stability assurance is not straightforward for distributed model predictive control (DMPC), since the well-known terminal cost and constraint technique cannot be readily adapted to the distributed schemes. An alternative method to the complicated procedure of splitting the terminal cost function and constraint set to achieve stability, is to calculate a minimum length for the DMPC prediction horizon. It is known that the DMPC cost will then have a relationship to the infinite-horizon cost, which is determined by a so-called performance factor. Moreover, the stopping condition of the distributed optimization algorithm, which for the sake of smooth handling of the coupling constraints is usually a duality-based algorithm, can be formulated using two scalars: an upper bound for the cost of the next sampling period and a lower bound for the optimal cost of the current one. For the duality-based algorithms, feasibility can only be guaranteed in the limit of iterations, thus the constraint tightening technique should be employed to determine the former scalar. The tightening technique, however, impinges upon calculation of the latter one. This problem is already addressed in the literature for gradient-based methods. By contrast, the consensus form of alternating direction method of multipliers (ADMM) is employed in this paper to stabilize the DMPC scheme. Simulation results reveal that this method outperforms the existing gradient-based approaches in terms of the required number of communications.