Desired Compensation Adaptive Robust Control

A desired compensation adaptive robust control (DCARC) framework is presented for nonlinear systems having both parametric uncertainties and uncertain nonlinearities. The paper first considers a class of higher order nonlinear systems transformable to a normal form with matched model uncertainties. For this class of uncertain systems, the desired values of all states for tracking a known desired trajectory can be predetermined and the usual desired compensation concept can be used to synthesize DCARC laws. The paper then focuses on systems with unmatched model uncertainties, in which the desired values of the intermediate state variables for perfect output tracking of a known desired trajectory cannot be pre-determined. A novel way of formulating desired compensation concept is proposed and a DCARC backstepping design is developed to overcome the design difficulties associated with unmatched model uncertainties. The proposed DCARC framework has the unique feature that the adaptive model compensation and the regressor depend on the reference output trajectory and on-line parameter estimates only. Such a structure has several implementation advan∗Part of the paper was presented in the 1998 ASME International Mechanical Engineering Congress and Exposition (IMECE). The work is supported in part by the US National Science Foundation (Grant No. CMS-0600516) and in part by the National Natural Science Foundation of China (NSFC) under the Joint Research Fund for Overseas Chinese Young Scholars (Grant No. 50528505). †Corresponding author: Bin Yao Address: Professor of School of Mechanical Engineering at Purdue University, West Lafayette, IN 47907, USA. Also a Kuang-piu Professor at the State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Hangzhou, China; e-mail:[email protected]