Sliding mode control for underactuated system with input constraint based on RBF neural network and Hurwitz stability analysis

The sliding mode control method is proposed for a class of underactuated systems with input constraint in this paper. The properties of hyperbolic tangent function are used to deal with input constraint. Furthermore, a radial basis function (RBF) neural network is adopted to achieve the approximation of the unknown function and the projection mapping operator is used to further guarantee the bounded approximation. The control law is designed by using the Lyapunov's direct method, and the stability is conducted by using Hurwitz stability analysis. In the simulation part, two examples are listed, including a simple underactuated system and an underactuated inverted pendulum system, which can all be transformed into the model style studied in this paper to illustrate the effectiveness of the proposed control law. At last, the conclusion is summarized.