Stochastic Model Predictive Control: An Overview and Perspectives for Future Research

TLDR

Model predictive control (MPC) has achieved high‑performance control of complex systems, owing to its conceptual simplicity and its capacity to manage multivariable dynamics, constraints, and conflicting objectives. This article reviews the past decade’s developments in stochastic model predictive control, outlining key algorithms and theoretical challenges, and proposes future research directions. The authors first present a general formulation of a stochastic optimal control problem, then survey SMPC methods for both linear and nonlinear systems.

Abstract

Model predictive control (MPC) has demonstrated exceptional success for the high-performance control of complex systems. The conceptual simplicity of MPC as well as its ability to effectively cope with the complex dynamics of systems with multiple inputs and outputs, input and state/output constraints, and conflicting control objectives have made it an attractive multivariable constrained control approach. This article gives an overview of the main developments in the area of stochastic model predictive control (SMPC) in the past decade and provides the reader with an impression of the different SMPC algorithms and the key theoretical challenges in stochastic predictive control without undue mathematical complexity. The general formulation of a stochastic OCP is first presented, followed by an overview of SMPC approaches for linear and nonlinear systems. Suggestions of some avenues for future research in this rapidly evolving field concludes the article.