A non-recursive C1 adaptive stabilization methodology for nonlinearly parameterized uncertain nonlinear systems

A non-recursive adaptive stabilization method, under a semi-global stability objective, is studied in this paper for a class of nonlinearly parameterized uncertain nonlinear systems. By incorporating the homogeneous system theory and a non-recursive synthesis approach, the resulting C1 adaptive stabilizing control scheme can now be constructed within a novel one-step design framework. Employing an adaption law to online determine the time-varying scaling gain, both the controller expression and gain tuning mechanism are much simpler than related existing recursive design approaches. It is also shown that the proposed method will be applicable to a class of non-triangular nonlinear uncertain systems. Besides, considering a smooth control case, a C1 condition of the system nonlinearities is sufficient for deriving an effective linear adaptive stabilizing control scheme. Examples and numerical simulations are provided to demonstrate both the simplicity and effectiveness of the proposed control algorithms.