Learning from adaptive neural control for a class of pure-feedback systems

This paper studies learning from adaptive neural control (ANC) for a class of pure-feedback nonlinear systems with unknown non-affine terms. The existence of the cascade structure and unknown non-affine terms makes it very difficult to achieve learning using previous methods. To overcome these difficulties, firstly, the implicit function theorem and the mean value theorem are combined to transform the closed-loop system into a semi-affine form during the control design process. Then, we decompose the stable closed-loop system into a series of linear time-varying (LTV) perturbed subsystems with the appropriate state transformation. Using a recursive design, the partial persistent excitation (PE) condition for the radial basis function (RBF) neural network (NN) is satisfied during tracking control to a recurrent reference trajectory. Under the PE condition, accurate approximations of the closed-loop system dynamics are recursively achieved in a local region along recurrent orbits of closed-loop signals. Subsequently, the NN learning control method which effectively utilizes the learned knowledge without re-adapting to the unknown system dynamics is proposed to achieve the closed-loop stability and the improved control performance. Simulation studies are performed to demonstrate the effectiveness of the proposed scheme.