Adaptive control of uncertain pure-feedback nonlinear systems

An adaptive control approach is proposed to solve the globally asymptotic state stabilisation problem for uncertain pure-feedback nonlinear systems which can be transformed into the pseudo-affine form. The pseudo-affine pure-feedback nonlinear system under consideration is with nonlinearly parameterised uncertainties and possibly unknown control coefficients. Based on the parameter separation technique, a novel backstepping controller is designed by adopting the adaptive high gain idea. The proposed control approach could avoid the drawbacks of the approximation-based approaches since no estimators are needed to estimate the virtual and the actual controllers. In addition, it could guarantee globally asymptotic state stabilisation even though there exist nonlinearly parameterised uncertainties in the considered system while comparing to the existing approximation-free approaches. A numerical and a realistic examples are employed to demonstrate the effectiveness of the proposed control method.