New results on explicit adaptive control design for nonlinear systems with polynomial conditions

This paper discusses the adaptive control problem for a class of nonlinear systems with polynomial growing conditions. By introducing a Lyapunov function which carries the quadratic terms and higher-order terms of the transformed variables and constructing an appropriate dynamic gain, a new control strategy is presented to design an adaptive controller using only one parameter estimation. Compared with the existing results, the presented method avoids the over-parameterization and significantly simplifies the control design. A modified version of the method which adopts no parameter estimation is also provided. It shows that all the signals of the closed-loop system are bounded and the solution of the original system converges to zero. A simulation example is given to show the validness of the method.