Model Predictive Control in Dynamic Systems

Model Predictive Control (MPC) is an optimisation-based strategy that forecasts system behaviour over a finite horizon and computes control actions by solving a constrained optimisation problem at each sampling instant. By leveraging an explicit dynamic model, MPC can handle multivariable interactions, input and state constraints, and time-varying objectives. Recent advances have extended its scope to nonlinear and large-scale systems, integrated economic performance criteria directly into the control formulation, and developed robust variants that account for uncertainty and disturbances. Computational improvements, including tailored solvers and hardware acceleration, have enabled real-time deployment in applications ranging from chemical process plants and energy systems to autonomous vehicles and power grid management. The global significance of MPC is underscored by its ability to improve safety, efficiency and sustainability across diverse industrial and environmental domains.

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Research from all publishers

Recent studies have expanded MPC frameworks to dynamic operations, introducing generalised formulations that accommodate time-varying objectives and constraints, enabling applications that range from set-point tracking to economic optimisation under fluctuating conditions. A comprehensive review of these frameworks highlights methods for nonlinear constrained systems, assesses computational strategies for recursive feasibility, and outlines opportunities to improve adaptability in real-time settings. Another line of work integrates safe transfer-learning techniques into MPC for nonlinear processes, leveraging pretrained task knowledge to accelerate controller synthesis while enforcing safety through invariant sets; successful demonstrations have been reported in chemical plant case studies. Advances in predictive modelling have employed recurrent neural networks—particularly LSTM and GRU architectures—to capture complex dynamics and deliver data-driven MPC schemes that reduce modelling effort and achieve control performance comparable to first-principles approaches with reduced computational overhead.

Model Predictive Control in Dynamic Systems publication trend

The graph below shows the total number of articles in model predictive control in dynamic systems across all publications each year (not limited to Nature Index journals).

Technical terms

Model Predictive Control (MPC): An optimisation-based control strategy that predicts future system behaviour over a finite horizon to determine current control inputs.

Prediction horizon: The future time interval over which the system’s behaviour is forecast and optimised.

Constraint optimisation: The process of finding control actions that satisfy physical and operational limits while optimising a specified performance criterion.

Tube-based MPC: A robust MPC technique that maintains the system trajectory within a bounded region (“tube”) to ensure constraint satisfaction under disturbances.

Economic MPC: A variant of MPC where the objective function reflects an economic or operational cost metric rather than solely tracking errors.

References

1. Analysis and design of model predictive control frameworks for dynamic operation—An overview. Annual Reviews in Control (2024).
2. Safe Transfer-Reinforcement-Learning-Based Optimal Control of Nonlinear Systems. IEEE Transactions on Cybernetics (2024).
3. Review on model predictive control: an engineering perspective. The International Journal of Advanced Manufacturing Technology (2021).
4. A software framework for embedded nonlinear model predictive control using a gradient-based augmented Lagrangian approach (GRAMPC). Optimization and Engineering (2019).
5. Advanced predictive control for GRU and LSTM networks. Information Sciences (2022).