Tracking and Almost Disturbance Decoupling for Nonlinear Systems with Uncertainties

Abstract

This paper studies the output tracking and almost disturbance decoupling problem of nonlinear control systems with uncertainties. The main contribution of this study is to construct a controller, under appropriate conditions, such that the resulting closed-loop system is valid for any initial condition and bounded tracking signal with the following characteristics: input-to-state stability with respect to disturbance inputs and almost disturbance decoupling, i. e., the influence of disturbances on the L₂ norm of the output tracking error can be arbitrarily attenuated by changing some adjustable parameters. The fundamental theoretical approaches are the differential geometry approach and the composite Lyapunov approach. Two examples, which cannot be solved by the first paper on the almost disturbance decoupling problem, are proposed in this paper to exploit the fact that the tracking and the almost disturbance decoupling performances are easily achieved by the proposed approach. In order to demonstrate the practical applicability, the paper has investigated a pendulum control system that cannot be solved by some existent approaches.