Model Predictive Control: Theory, Implementation and Algorithmic Approaches

Model Predictive Control (MPC) is an advanced control strategy based on system dynamic models, widely applied in industrial process control, robotic motion planning, and other domains. Its core principle involves solving optimal control sequences over a finite future horizon through online receding horizon optimization. In code implementation, this typically requires maintaining a prediction window and solving quadratic programming problems at each time step.

The standard MPC implementation involves three key algorithmic steps: First, establishing a system prediction model (such as state-space equations or transfer functions) to predict future system dynamics - often implemented using discrete-time models with functions like `ss()` for state-space representation in MATLAB. Second, designing an objective function (typically containing tracking error and control effort penalty terms) and solving the optimization problem - commonly implemented using quadratic programming solvers like `quadprog()` with proper constraint handling. Third, applying the receding horizon strategy where only the current optimal control action is executed, followed by re-optimization at the next sampling period using updated measurements.

The advantages of this control method include explicit handling of multivariable coupling and constraints (such as actuator saturation), while improving robustness through feedback correction. Its practical utility is demonstrated through relative tolerance to model accuracy requirements and the ability to balance computational complexity with control performance by adjusting parameters like prediction horizon and control horizon. Modern MPC has evolved into linear/nonlinear variants, incorporating fast optimization algorithms such as active-set methods or interior-point solvers to meet real-time requirements in embedded systems.