Nonlinear Model Predictive Control

Nonlinear Model Predictive Control (NMPC) is a predictive control methodology based on nonlinear dynamic models, extensively employed for control and optimization of complex systems. Compared with linear model predictive control, its core distinction lies in handling nonlinear characteristics within system dynamics, making it particularly suitable for strongly nonlinear scenarios such as chemical processes and robotic trajectory planning.

Typical implementation follows a three-step framework: Dynamic Modeling: Establish mathematical models that capture system nonlinear behaviors, potentially involving differential equations or data-driven black-box models. Implementation often requires numerical integration methods like Runge-Kutta for continuous systems or neural networks for data-driven approaches; Receding Horizon Optimization: Solve control inputs in real-time through numerical optimization techniques (such as gradient descent, Sequential Quadratic Programming) within a finite prediction horizon, balancing objective functions with constraint conditions. Code implementation typically involves optimization solvers like IPOPT or CasADi for efficient constraint handling; Feedback Correction: Incorporate actual outputs and prediction errors to recursively update model parameters, enhancing system robustness. This often involves state estimation algorithms like Extended Kalman Filter or moving horizon estimation for parameter adaptation.

Key challenges include high computational complexity and stringent real-time requirements, frequently addressed through reduced-order models or parallel computing optimizations. Future directions may explore hybrid data-model driven strategies or improved algorithms tailored for specific scenarios like time-delay systems, potentially leveraging machine learning techniques for enhanced performance.