Efficient Nonlinear MPC by Leveraging LPV Embedding and Sequential Quadratic Programming

In this paper, we present efficient solutions for the nonlinear program (NLP) associated with nonlinear model predictive control (NMPC) by leveraging the linear parameter-varying (LPV) embedding of nonlinear models and sequential quadratic programming (SQP). The corresponding quadratic program (QP) subproblem is systematically constructed and efficiently updated using the scheduling parameter from the LPV embedding, enabling fast convergence while adapting to the behavior of the controlled system. The method integrates the SQP approach into the LPV-MPC formulation based on inexact Hessians/Jacobians. Furthermore, the approach provides insight into the problem, its connection to SQP, and a clearer understanding of the differences between solving NMPC as an NLP and using the LPV-MPC approach, compared to similar methods in the literature. The efficiency of the proposed approach is demonstrated against state-of-the-art methods, including NLP algorithms, in control benchmarks and practical applications.