Direct Adaptive Control for a Certain Class of Nonlinear Systems Using Modified Radial Basis Function Neural Network

This paper proposes a direct adaptive controller for SISO affine nonlinear systems using Gaussian radial basis function (RBF) neural network (NN). The exact plant model is not necessary for composing the controller. If the plant is SISO, of affine form, without zero dynamics, and all the state variables are available, the controller is applicable under several mild assumptions. In this paper, the Gaussian RBF network (GRBFN) is modified to include pre-scale weights as its parameters for the input variables, which are also adapted in the control law. Pre-scaling the inputs is equivalent to extending or contracting the spectrum of the approximated function. With the modification, the spectrum along each coordinate of the domain can be scaled separately for approximating. The adaptation of the nonlinear parameters, including the variances, centers, and pre-scaling weights, are derived. Appropriate modification techniques are applied to the adaptation laws to ensure the robustness. The stability is analyzed with Lyapunov’s Theory. From the analysis, the effect of the controller design parameters is also examined. A simulation of an inverted pendulum control is demonstrated to show the effectiveness.