Hierarchical Distributed Model Predictive Control based on Dual Decomposition and Quadratic Approximation

This paper presents a dual decomposition-based distributed optimization algorithm and applies it to distributed model predictive control (DMPC) problems. The considered DMPC problems are coupled through shared limited resources. Lagrangian duality can be used to decompose an MPC problem, so that each subsystem can compute its individual resource utilization, without sharing information, such as dynamics or constraints, with the other subsystems. The feasibility of the central problem is ensured by the coordination of the subproblems through dual variables which can be interpreted as prices on the shared limited resources. The proposed coordination algorithm makes efficient use of information collected from previous iterations by performing a quadratic approximation of the dual function of the central MPC problem. Aggressive update steps of the dual variables are prevented through a covariance-based step size constraint. The nonsmoothness encountered in dual optimization problems is addressed by the construction of cutting planes, similar to bundle methods for nonsmooth optimization. The cutting planes ensure that the updated dual variables do not lie outside the range of validity of the dual approximation. The proposed algorithm is evaluated on a two-tank system and compared to the standard subgradient method. The results show that the rate of convergence towards the centralized solution can be significantly improved while still preserving privacy between the subsystems through limited information exchange.