Due to their considerable practical importance, fast nonlinear predictive control schemes have been receiving considerable attention over the last two decades. In this talk we present a recently developed approach to nonlinear MPC that is based on a quasi-Linear Parameter-Varying (qLPV) model of the plant. The nonlinear optimization problem is solved by iteratively optimizing the input sequence for an LTV system (using warm starts, this typically amounts to solving one QP per sampling period). Stability can be guaranteed via terminal constraints.

When a first-principles model of the nonlinear plant is available, a suitable qLPV model can be constructed using a velocity-linearisation approach. Alternatively, when a first-principles model is not available, we present a data-driven approach to construct a qLPV model that is based on a truncated Koopman operator representation and can be updated online. The real-time capability of the proposed method is illustrated with experimental results on an arm-driven inverted pendulum, a robot manipulator and a control moment gyroscope.