Model Predictive Control Based on State-Space Models

State-space models combined with Model Predictive Control (MPC) algorithms achieve exceptional control performance for dynamic systems. State-space models serve as a mathematical framework widely adopted in control systems to characterize complex dynamic behaviors. MPC represents an advanced control methodology that optimizes future system behavior through predictive computations. This approach typically involves solving a constrained optimization problem at each time step using quadratic programming, where the cost function minimizes tracking errors and control efforts over a finite prediction horizon. The controller employs system matrices (A, B, C, D) for state propagation and output prediction, while incorporating constraints handling through algorithms like active-set or interior-point methods. Beyond traditional control applications, this methodology finds implementations in robotics trajectory planning, autonomous vehicle path following, and industrial process control. The integration of state-space modeling with MPC not only ensures efficient system regulation but also offers broad applicability across modern control domains.