Global stabilization for feedforward nonlinear systems with unknown control direction and unknown growth rate

This paper investigates the global adaptive state feedback controller design for a class of feedforward nonlinear systems with completely unknown control direction and unknown growth rate. Since the control direction, i.e., the sign of the control coefficient, is unknown, the control problem becomes much more challenging, to which a Nussbaum-type function is exploited. Moreover, the systems heavily depend on the unmeasured states with unknown growth rate, and hence a dynamic gain, rather than a constant one, is adopted to compensate the large system unknowns. For control design, 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 and a dynamic high gain. It is shown that the state of the original system converges to zero, while the other states of the closed-loop system are globally bounded. Finally, a simulation example is provided to illustrate the effectiveness of the theoretical results.