A computationally efficient parallel coordinate descent algorithm for MPC: Implementation on a PLC

In this paper we propose a parallel coordinate descent algorithm for solving smooth convex optimization problems with separable constraints that may arise e.g. in model predictive control (MPC) for linear network systems. The basis for the new algorithm are block coordinate descent updates, that are computed in parallel, have low iteration complexity and use only local information. As a result, the algorithm is suitable for implementation on autonomous hardware with low computational power. In the case of a strongly convex objective function, we prove that the algorithm has linear rate of convergence. An MPC scheme based on this algorithm is derived, such that the computations of feasible and stabilizing inputs are distributed and cheap, and can be done by each subsystem in part. Some implementation issues of the new algorithm for MPC problems are discussed, as well as it being tested on a 4 tank laboratory setup.