This paper addresses the tracking control problem of nonstrict-feedback systems with unknown control gains. The dynamic surface control method, Nussbaum gain function control technique, and radial basis function neural network are applied for the design of virtual control laws, and adaptive control laws. Then, an adaptive neural tracking control law is proposed in the last step. By using the dynamic surface control method, the “explosion of complexity” problem of conventional backstepping is avoided. Based on the application of the Nussbaum gain function control technique, the unknown control gain problem is well solved. With the help of the radial basis function neural network, the unknown nonlinear dynamics are approximated. Furthermore, through Lyapunov stability analysis, it is proved that the proposed control law can guarantee that all signals in the closed-loop system are bounded and the tracking error can converge to an arbitrarily small domain of zero by adjusting the design parameters. Finally, two examples are provided to illustrate the effectiveness of the proposed control law.

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This work studies the asymptotic tracking control problem of a vertical take-off and landing (VTOL) aircraft with unknown dynamics and external disturbances. The unknown nonlinear dynamics of the VTOL aircraft are approximated via the introduction of radial basis function neural networks. Then, the weight update laws are designed. Furthermore, the parameter update control laws are presented to deal with the errors generated during the approximation process and the external disturbances of the aircraft system. Moreover, first-order filters are introduced to avoid repeated differentiation of the designed virtual control laws, thereby effectively eliminating the “complexity explosion” problem caused by traditional backstepping control. Based on the application of the neural network control method, dynamic surface control technique, weight update laws and parameter update control laws, neuroadaptive dynamic surface control laws for the aircraft system are finally proposed. Theoretical analysis shows that the proposed control law can ensure that the aircraft system asymptotically tracks the reference trajectories and the tracking errors can converge to a small neighborhood of zero by choosing the appropriate designed parameters. Finally, simulation examples are provided to verify the effectiveness of proposed control laws.