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This lecture covers the application of Real-Time Nonlinear Model Predictive Control (NMPC) in fast mechatronic systems, addressing key challenges such as complex dynamics, high sampling rates, and limited computational resources. The instructor discusses the flexibility of NMPC as a control framework, its ideal requirements, and the use of PolyMPC library for embedded optimization. The lecture also explores the basics of Pseudospectral Collocation, Quadratic Programming, and the Alternating Directions Method of Multipliers. Practical examples include NMPC applications in rocket thrust vector control, autonomous parking, and racing, showcasing the advantages of NMPC in handling complex dynamics and achieving optimal performance.