On the Design of Terminal Ingredients in Periodic Model Predictive Path‐Following

ABSTRACT Establishing recursive feasibility and convergence for nonlinear model predictive path‐following control (MPPFC) is a non‐trivial task, particularly when following periodic reference paths. We propose a procedure for the design of terminal ingredients in MPPFC for constrained nonlinear systems. In MPPFC, the system is augmented by a progress dynamics and a virtual control input, the progress velocity , which serves as an additional decision variable in the optimization problem. Unlike standard time‐based tracking MPC, this allows the controller to optimize the timing law itself. Based on a periodic path in the state space and a corresponding nominal timing law, we construct a periodically time‐varying quadratic terminal cost and an associated ellipsoidal terminal region by linearizing the dynamics along the nominal trajectory and solving a periodic Riccati differential equation. By reparameterizing these time‐dependent ingredients with respect to the progress variable, we obtain a progress‐varying terminal cost and terminal region suitable for path‐following. Furthermore, we prove that the resulting scheme is recursively feasible, guarantees convergence of the error to zero, and ensures convergence of the progress velocity to its nominal reference. The applicability of the approach is demonstrated on a 2D nonlinear system.