MPC (Model-Predictive Control)

Model-Predictive Control (MPC) is an optimization-based control strategy that uses an explicit mathematical model of a system to predict its future behavior and compute optimal control actions accordingly. At each time step, MPC solves a constrained optimization problem over a finite prediction horizon, selecting the sequence of control inputs that minimizes a defined cost function — such as tracking error or energy consumption — while satisfying physical and operational constraints. Only the first action in the optimal sequence is applied, after which the horizon rolls forward and the process repeats. This receding-horizon structure allows MPC to continuously adapt to new information and disturbances.

The power of MPC lies in its ability to handle multivariable systems with hard constraints on inputs and outputs in a principled, unified framework. Unlike classical control methods that treat constraints as afterthoughts, MPC incorporates them directly into the optimization, making it well-suited for systems where safety limits, actuator saturation, or resource bounds are critical. The underlying optimization is typically a quadratic program for linear systems, though nonlinear variants (NMPC) exist for more complex dynamics at greater computational cost.

In machine learning and reinforcement learning, MPC has gained renewed relevance as a planning and decision-making backbone. Model-based reinforcement learning methods often use learned dynamics models within an MPC loop, enabling sample-efficient control without requiring a hand-engineered model. Techniques like the Cross-Entropy Method (CEM) or random shooting are used to approximately solve the MPC optimization when gradients are unavailable or the model is a neural network. This intersection has made MPC a central component in modern robotics, autonomous driving, and continuous control benchmarks.

MPC's practical appeal stems from its interpretability and constraint-handling, properties that purely learned policies often lack. As learned world models improve in accuracy and inference speed, hybrid approaches combining the flexibility of deep learning with the structure of MPC are increasingly common, positioning MPC as a durable and adaptable tool at the frontier of intelligent control systems.