Fast gradient-based distributed optimisation approach for model predictive control and application in four-tank benchmark

By taking both control and state vectors as decision variables, the subproblems of model predictive control scheme can be considered as a class of separable convex optimisation problems with coupling linear constraints. A Lagrangian dual method is introduced to deal with the optimisation problem, in which, the primal problem is solved by a parallel coordinate descent method, and a fast dual ascend method is adopted to solve the dual problem iteratively. The proposed approach is applied to the well-known hierarchical and distributed model predictive control four-tank benchmark. Experimental results have testified the effectiveness of the proposed approach and shown that the benchmark problem can be well stabilised.