Adaptive stabilization for feedforward nonlinear systems with unknown control direction

This paper investigates the global adaptive stabilization by state feedback for a class of feedforward nonlinear systems with completely unknown control coefficient. To the best of our knowledge, none of the work for the problem has been published up to now. Since the control direction, i.e., the sign of the control coefficient, is unknown, the Nussbaum gain function is used to deal with it. For control convenience, a suitable state transformation is first introduced for the original system. Then, the state feedback controller is proposed based on an appropriate Nussbaum-type function. It is shown that the state of the original system converges to zero while the other sates of the closed-loop system are globally bounded. Finally, a simulation example is given to illustrate the correctness of the theoretical results.