A General Dynamic Scaling Based Control Redesign to Handle Input Unmodeled Dynamics in Uncertain Nonlinear Systems

A general class of uncertain nonlinear systems with dynamic input uncertainties (nonlinear input unmodeled dynamics) is considered. While the proposed approach can, in general, be applied to multi-input systems, single-input systems are considered here for simplicity. It is shown that if a nominal control law is available to globally asymptotically stabilize the nominal system (without the input unmodeled dynamics), then a dynamic scaling based redesign of the control law can be performed to achieve global asymptotic stabilization of the system with the input unmodeled dynamics. The proposed control redesign approach is applicable to a wide class of nonlinear systems including triangular and non-triangular structures as long as a set of structural and inequality conditions on the system dynamics is satisfied and yields a global robust output-feedback stabilizing controller.