Nonlinear PI Control of Uncertain Systems

Abstract

A novel approach to stabilisation and trajectory tracking for nonlinear systems with unknown parameters and uncertain disturbances is developed in this chapter. We depart from the classical adaptive control approach consisting of a parameterised feedback law and an identifier, which tries to minimise a tracking (or prediction) error. Instead, we propose a simple nonlinear proportional-integral (PI) structure that generates a stable error equation—similar to the off-the-manifold dynamics obtained in the I&I approach—with a perturbation function that exhibits at least one root. Trajectories are forced to converge to this root by suitably adjusting the proportional and integral gains of the nonlinear PI controller.