Identification of nonlinear dynamical system based on adaptive radial basis function neural networks

In this paper, an adaptive radial basis function neural network (RBFNN) is investigated and presented for identifying the nonlinear dynamical system. In traditional RBFNN structure, the selections of the activated radius are decided by the designer’s experience to satisfy the best approximation of nonlinear dynamical function. In order to reduce the experience error, an adaptive RBFNN mechanism that can realize auto-regulation of activated radius is proposed in this paper. Taking the lattice points as the center of activated function, we use Taylor expansion to separate the factor of activated radius in local space. In order to ensure that the identification error has the property of fast convergence, the error conversion function is used for shrinking the gain in the error differential equation. Constructing a Lyapunov function to determine the differential equation of the weights and the activated radius, it is shown that the weights and the activated radius will converge to the neighborhood of its true value and the identification error will converge to neighborhood of zero in a periodic or period-like nonlinear dynamical system. To illustrate the effectiveness of the proposed adaptive RBFNN, Vanderpol and Duffing dynamical system are used as test examples, in comparison with traditional RBFNN and wavelet neural networks (WNN). The results show that the proposed method has best accurate identification and approximating effect in all of test algorithms.