Efficient NMPC of unstable periodic systems using approximate infinite horizon closed loop costing

Abstract

We develop a state-of-the-art nonlinear model predictive controller (NMPC) for periodic unstable systems, and apply the method to a dual line kite that shall fly loops. The kite is described by a nonlinear unstable ODE system (which we freely distribute), and the aim is to let the kite fly a periodic figure. Our NMPC approach is based on the “infinite horizon closed loop costing” scheme to ensure nominal stability. To be able to apply this scheme, we first determine a periodic LQR controller to stabilize the kite locally in the periodic orbit. Then, we formulate a two-stage NMPC optimal control problem penalizing deviations of the system state from the periodic orbit, which also contains a state constraint that avoids that the kite collides with the ground. To solve the optimal control problems reliably and in real-time, we apply the newly developed “real-time iteration scheme” for fast online optimization in NMPC. The optimization based NMPC leads to significantly improved performance compared to the LQR controller, in particular as it respects state constraints. The NMPC closed loop also performs well in the presence of large random disturbances and shows considerable robustness against changes in the wind direction.