Robust adaptive neural control for a class of non-affine nonlinear systems

This paper addresses the adaptive neural tracking control problem for a class of uncertain non-affine nonlinear system with non-affine function being semi-bounded and possibly non-differentiable. Compared with traditional control schemes, the proposed scheme can be applied to a more general class of non-affine nonlinear system, and relaxes constraint conditions as follows: firstly, the assumption that non-affine function must be differentiable is canceled, and only a continuous condition for non-affine function is required to guarantee the controllability of the considered system, secondly, the assumption that non-affine function is completely bounded is relaxed, and the non-affine function is constrained by a semi-bounded condition with the bounds being unknown functions. Then, an adaptive neural tracking controller is designed based on an invariant set. In the control design process, minimal learning parameter (MLP) technique is used to reduce the number of adaptive parameters, and a smooth robust compensator is employed to circumvent the influences of approximation error and external disturbance. Furthermore, it is proven that all the closed-loop signals are semi-globally uniformly ultimately bounded. Finally, simulation examples are provided to demonstrate the effectiveness of the designed method.