Global exact tracking for nonlinear systems: A novel non-recursive design framework

Abstract

In this paper, a non-recursive control design method is addressed to solve the exact (practical) tracking problem for a class of inherent nonlinear systems. By introducing a series of coordinates transformation via an output regulation technique, a new one-step design strategy is made feasible by virtue of utilizing the homogeneous system theory. First, a concise stabilizing control law is constructed in a quasi-linear form for the nominal chain of integrators, whose effectiveness is guaranteed by an explicit stability analysis. Second, a scaling gain performed as a bandwidth factor is introduced into the original system and hence the homogeneous domination strategy is applied to derive a robust tracking control law. By proceeding with a rigorous non-recursive stability analysis framework which covers both global asymptotical and finite-time convergence cases, the common recursively treated derivative items in backstepping based design methods are totally avoided while the proposed control performance can be guaranteed. In the case when system is disturbed by bounded mismatched disturbances, it is shown that a global practical tracking control result can be achieved with the same design procedure. Numerical examples and their control performance simulations are given to illustrate the effectiveness and simplicity of the proposed design framework.