A Parallel Algorithm of Stochastic Model Predictive Control by Partial Minimization

ABSTRACT This article proposes a parallel algorithm of stochastic model predictive control (SMPC) for linear discrete‐time systems. The proposed algorithm uses multiple threads to solve respective optimization problems at different time steps in parallel, without inter‐thread communication during each optimization. Each thread sequentially solves a stochastic optimal control problem (SOCP) for optimizing closed‐loop performance against future disturbances and a partial minimization problem for optimizing a subset of decision variables of the SOCP. The partial minimization problem computes the control input according to the last measured state to satisfy chance constraints and can be solved much faster than the original SOCP. Consequently, the proposed algorithm can reduce the implementable minimum sampling period compared to the original SMPC. A numerical example of controlling room temperature showed that the proposed algorithm achieves control performance almost identical to that of closed‐loop SMPC, which optimizes closed‐loop performance. However, the implementable minimum sampling period of the proposed algorithm is much shorter than that of the closed‐loop SMPC, even with parallelization overhead.