Predictive control of fast unstable and nonminimum-phase nonlinear systems

The problem of controlling fast, unstable, and nonminimum-phase systems is considered. With standard predictive control, the time required for optimization is typically larger than the sampling interval that is needed for stabilization of the fast dynamics. On the other hand, due to the nonminimum-phase behavior, control based on input-output feedback linearisation leads to unstable internal dynamics. In the paper, a cascade structure is proposed, with control based on input-output feedback linearisation forming the inner loop and predictive control the outer loop. Assuming high-gain feedback for the inner loop, a stability analysis of the global scheme is provided based on singular perturbation theory. The approach is illustrated via the simulation of an inverted pendulum system.