A Novel Iss-modular Adaptive Neural Control of Pure-feedback Nonlinear Systems

In this paper, an ISS-modular adaptive neural tracking control approach is presented for a class of completely non-affine pure-feedback systems combining backstepping with input-to-state stability (ISS) and small gain theorem. From the second step of backstepping, correlative interconnection terms are defined and introduced in implicit functions. Since the introduction of the correlative interconnection terms does not add any variable, radial basis function (RBF) neural networks are still valid to approximate the implicit functions as the existing results. Subsequently, the construction of the quadratic-type ISS-Lyapunov function makes the correlative interconnection terms completely eliminate the interconnected terms, so that ISS neural controller design is simplified by the combination of the small gain theorem. The proposed approach not only overcomes the difficulty in controlling non-affine pure-feedback systems, but also simplifies the stability analysis of the closed-loop system. Simulation studies are performed to demonstrate the effectiveness of the proposed scheme.