Adaptive control for a class of time-varying uncertain nonlinear systems

This paper develops an adaptive nonlinear control scheme for time-varying parametric uncertain nonlinear system with completely unknown time-varying bounded control coefficient. The proposed design method does not require any a priori knowledge of the sign of the unknown time-varying control coefficient, based on incorporating Nussbaum function gain and smooth projection allgorithm into backstepping. It is proved that the designed adaptive nonlinear controller can guarantee the stability and the global uniform ultimate boundedness of all signals of the resulting closed-loop system. The control performances of the system can be guaranteed by an appropriate choice of the design parameters. Simulation studies are included to illustrate the feasibility and effectiveness of the presented approach.