Model predictive control strategies using consensus-based optimization

Model predictive control strategies require to solve in a sequential manner, many, possibly non-convex, optimization problems. In this work, we propose an interacting stochastic particle system to solve those problems. The particles evolve in pseudo-time to control the time-discrete state evolution. The method is gradient-free and aims to find global minima to the objective functions. The convergence properties are investigated in the case of input-affine control and a one-step prediction horizon, through a mean-field approximation of the time-discrete system. We validate the proposed strategy by applying it to the control of a linear time-invariant model and a stirred-tank reactor non-linear system.