Stabilizing Distributed Model Predictive Control using the Consensus Form of ADMM

In distributed model predictive control (DMPC) problems, stability assurance is a demanding issue since the well-known terminal cost and constraint technique is not readily adaptable to the distributed schemes. An alternative to the complex procedure of calculating a separable terminal cost function and constraint set for stabilization is to quantify a minimum length for the DMPC prediction horizon. It is known that with such a stabilizing horizon length the DMPC cost bears a relationship to the infinite-horizon cost through a so-called performance factor. The stopping criterion of the distributed optimization algorithm, which for the sake of smooth handling of the coupling constraints is usually a duality-based algorithm, can then be assessed by determination of 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. Since in duality-based algorithms feasibility can only be attained in the limit of iterations, the constraint tightening technique can be deployed to determine the former scalar. However, the tightening technique impinges upon computation of the latter one. This problem is already conquered in the literature for gradient-based methods. By contrast, in the current paper the consensus form of ADMM is utilized to deal with the DMPC problem and an iterative algorithm is introduced to determine the aforementioned lower bound with the aim of stabilizing DMPC. Simulation results reveal that this algorithm outperforms the existing gradient-based methods in terms of required number of iterations and communications.