Model Predictive Control
Also known as: MPC, Receding Horizon Control
Model Predictive Control (MPC) is an advanced control strategy that uses an explicit process model to predict future system behavior over a finite horizon and solves an optimization problem at each control step. First formalized by Richalet et al. in 1978, MPC has become the dominant approach in process control industries, from chemical plants to autonomous vehicles, because it naturally handles constraints and can optimize multiple objectives simultaneously.
Key highlights
- Naturally handles input and state constraints through explicit optimization.
- Provides multivariable control, coordinating multiple inputs and outputs automatically.
- Robust to disturbances and model mismatch because of the receding horizon feedback loop.
- Allows incorporation of future reference trajectory or set-point changes.
- Easy to tune (cost function weights) compared to traditional PID tuning.
Intuition
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How it works
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When to use it
Use MPC when you need to handle constraints explicitly (e.g., valve limits, safety bounds), manage multiple correlated variables (multivariable control), or when disturbances and non-linearities are significant. It is most effective for systems with slow to moderate dynamics where computation time allows for real-time optimization. Typical applications include chemical process control, HVAC systems, power plants, and autonomous driving. Avoid MPC if your system demands microsecond control rates or if a high-fidelity process model is unavailable.
Strengths & limitations
- Naturally handles input and state constraints through explicit optimization.
- Provides multivariable control, coordinating multiple inputs and outputs automatically.
- Robust to disturbances and model mismatch because of the receding horizon feedback loop.
- Allows incorporation of future reference trajectory or set-point changes.
- Easy to tune (cost function weights) compared to traditional PID tuning.
- Computationally expensive; solving the optimization problem at each step may be infeasible for very fast systems.
- Requires an accurate process model; poor model accuracy degrades performance significantly.
- Nonlinear MPC is non-convex and may get stuck in local minima.
- Stability and feasibility guarantees are non-trivial, especially for constrained problems.
Common pitfalls
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Applications
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Frequently asked
What is the receding horizon principle and why is it important?
The receding horizon principle means solving an optimization problem over a finite future window, applying only the first control action, and then shifting the window forward. This mechanism creates a feedback loop that corrects for errors and disturbances at each step, making MPC robust even when the model is not perfect.
How do I choose the prediction horizon length?
A rule of thumb is to set the prediction horizon to 3-5 times the settling time of the system's dominant time constant. Too short leads to myopic behavior; too long increases computation without additional benefit and may cause infeasibility. Empirical tuning or open-loop response analysis helps.
Can MPC handle nonlinear systems?
Yes, Nonlinear MPC (NMPC) can handle nonlinear system models. However, the optimization becomes non-convex, requiring iterative solvers that are slower and may converge to local minima. Linearization around a nominal trajectory or approximation methods are often used to reduce computation time.
What software tools are available for implementing MPC?
Popular tools include MATLAB Model Predictive Control Toolbox, Simulink, open-source packages like CasADi (for optimization), and specialized commercial platforms like EMSO and gProms. For embedded systems, libraries like ACADO and fast quadratic programming solvers (e.g., qpOASES) enable real-time implementation.
Sources
- 1.Richalet, J., Rault, A., Testud, J., & Papon, J. (1978). Model predictive heuristic control. Automatica, 14(5), 413-428.
- 2.Garcia, C. E., Prett, D. M., & Morari, M. (1989). Model predictive control: Theory and practice. Automatica, 25(3), 335-348.
- 3.Mayne, D. Q., Rawlings, J. B., Rao, C. V., & Scokaert, P. O. (2000). Constrained model predictive control: Stability and optimality. Automatica, 36(6), 789-814.
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Cite this page
ScholarGate. (2026, June 3). Model Predictive Control. ScholarGate. https://scholargate.app/control-theory/model-predictive-control