Dynamic gain–based neural network backstepping control with its applications to a quad-rotor hover

In this paper, a novel neural network (NN) backstepping control method is proposed for a class of uncertain nonlinear systems with unknown control direction functions. To solve the control problems caused by unknown control direction functions, a method called “virtual control coefficient” is presented using equivalence transformations. However, to improve the flexibility of the control method, a function named “dynamic gain” is introduced to design the feedback gains of the NN backstepping controllers. Moreover, instead of using σ-modification, gradient descent algorithm is applied to train the weights of NNs such that the unknown nonlinearities of the system can be well approximated by NNs. With the help of Lyapunov stability criterion, it can be proved that the system tracking error is semi-global uniformly ultimately bounded. Finally, the effectiveness of the proposed control method is verified by the experimental results on a quad-rotor hover platform.