A singular perturbation based approach for systems with nonlinear input uncertainties

A general class of uncertain nonlinear systems with input nonlinearities is considered. The system structure includes a core nominal system of triangular structure along with uncertain appended dynamics driven by the entire state of the system. The control input is allowed to enter non-affinely into the system dynamics as well as to have uncertainties coupled with it both in terms of an uncertain nonlinear function of the input and in terms of a dynamic perturbation due to uncertain appended dynamics. The control design is based on dual controller/observer dynamic high-gain scaling with an additional dynamic scaling based on a singular-perturbation-like redesign to address the non-affine and uncertain nature of the input appearance into the system dynamics. The proposed approach yields a global robust adaptive output-feedback control design. The application of the proposed control design approach to time-varying systems and systems containing uncertain state and input delays is also addressed, providing a delay-independent output-feedback control design.