Identification and learning control of strict-feedback systems using adaptive neural dynamic surface control

This paper focuses on identification and learning from adaptive neural dynamic surface control (DSC) for a class of nth-order strict-feedback systems. In the previous neural learning control proposed using backstepping, intermediate variables are often used as neural network (NN) inputs to keep the dimension of NN inputs minimal. However, the number and complexity of intermediate variables increase as the increasing order of the system. This makes it difficult to achieve learning for the high-order strict-feedback systems due to “the explosion of complexity”. To overcome the difficulty, a stable adaptive neural DSC is proposed with auxiliary first-order filters. Due to the use of DSC, the derivative of the filter output variable is used as the NN input instead of the previous intermediate variables. This reduces greatly the dimension of NN inputs, especially for high-order systems. After the stable DSC design, we decompose the stable closed-loop system into a series of linear time-varying (LTV) perturbed subsystems. Using a recursive design, the recurrent property of the NN input variables is easily proven since the complexity is overcome using DSC. Subsequently, the partial persistent excitation (PE) condition of the radial basis function (RBF) NN is satisfied. By combining a state transformation, accurate approximations of the closed-loop system dynamics are recursively achieved in a local region along recurrent orbits. Consequently, a neural learning control method with the learned knowledge is proposed to achieve the closed-loop stability and the better control performance with the faster tracking convergence rate and the smaller tracking error. Simulation studies are performed to demonstrate the effectiveness of the proposed scheme.