Model predictive control strategies using consensus-based optimization

TL;DR

This paper introduces a novel consensus-based stochastic agent system for model predictive control that effectively handles non-convex, non-differentiable optimization problems, with proven convergence and practical validation on a nonlinear reactor system.

Contribution

It proposes a new stochastic agent approach for MPC that converges under certain conditions and is suitable for complex, non-convex optimization problems.

Findings

Convergence demonstrated for linear control cases.

Method effectively applied to a stirred-tank reactor.

Handles non-convex, non-differentiable objectives.

Abstract

Model predictive control strategies require to solve in an sequential manner, many, possibly non-convex, optimization problems. In this work, we propose an interacting stochastic agent system to solve those problems. The agents evolve in pseudo-time and in parallel to the time-discrete state evolution. The method is suitable for non-convex, non-differentiable objective functions. The convergence properties are investigated through mean-field approximation of the time-discrete system, showing convergence in the case of additive linear control. We validate the proposed strategy by applying it to the control of a stirred-tank reactor non-linear system.