Approximate two‐loop robust nonlinear model predictive control with real‐time execution and closed‐loop guarantee

Abstract

In this article, a robust nonlinear model predictive control (NMPC) scheme with two control loops is considered and its real‐time execution is guaranteed for a predefined sampling time. Robustness of the NMPC scheme against bounded input uncertainty is achieved by assuming Lipschitz continuity of the inner‐loop dynamic function. The NMPC control law is approximated using piecewise affine linear functions over hyper‐rectangle regions generated by k‐d tree partitioning algorithm. Additionally, error bound on the approximation of the optimal solution function is obtained by assuming bounds on the subgradient of the optimal solution function. Consequently, the robust stability and recursive feasibility of the closed‐loop system for the proposed approximate NMPC framework are proven, and at the same time, real‐time execution of the proposed scheme for a predefined sampling time is guaranteed. Simulation results, on a nonlinear benchmark problem, are used to better illustrate the proposed approach and to compare it with some other methods.