Model Predictive Control: A Comprehensive Review of Theoretical Foundations and Modern Applications
Shuhan Liu
School of Physics Science and Technology, Shenyang Normal University, Shenyang 110031, China.
Zhirong Xiao
School of Physics Science and Technology, Shenyang Normal University, Shenyang 110031, China.
Tianbing Wang
School of Physics Science and Technology, Shenyang Normal University, Shenyang 110031, China.
Cheng Peng *
School of Food Science and Technology, Shenyang Normal University, Shenyang 110031, China.
*Author to whom correspondence should be addressed.
Abstract
Background: Model Predictive Control (MPC) is an optimization-based control strategy widely used for handling multivariable systems with constraints in industrial and autonomous applications. Recent advances integrating machine learning and data-driven approaches have expanded MPC’s capabilities, while raising new challenges related to real-time computation, robustness, and safety assurance.
Aims: This review aims to provide a comprehensive overview of the advancements in MPC from 2014 to 2026, highlighting key techniques, methodologies, and applications across robotics, autonomous systems, power electronics, industrial processes, and water resources systems.
Study Design: This review systematically analyzes the theoretical foundations, representative works, and ongoing challenges in MPC research.
Place and Duration of Study: Research findings span from 2014 to 2026, compiled from diverse academic sources.
Methodology: The study categorizes developments into classical MPC, robust/stochastic MPC, nonlinear/ economic MPC, data-driven/learning-based MPC, and real-time implementations. It examines significant papers related to these topics while summarizing challenges and future directions.
Results: The review reveals that MPC has significantly progressed in robustness, performance metrics, and real-time applications. Three major threads—robust/stochastic frameworks, data-driven adaptations, and economic optimizations—indicate a shift toward enhancing practical implementations and ensuring safety in dynamic environments.
Conclusion: The investigation concludes that maintaining the advantages of MPC in safety, constraint satisfaction, and interpretability is crucial while advancing towards learning and data-driven methodologies, creating a unified paradigm that bridges models, data, optimization, and safety.
Keywords: Model Predictive Control, rolling optimization, constrained control, robust and stochastic MPC, economic MPC, data-driven predictive control, real-time solver