Self-Organizing Radial Basis Function Network for Real-Time Approximation of Continuous-Time Dynamical Systems

Real-time approximators for continuous-time dynamical systems with many inputs are presented. These approximators employ a novel self-organizing radial basis function (RBF) network, which varies its structure dynamically to keep the prescribed approximation accuracy. The RBFs can be added or removed online in order to achieve the appropriate network complexity for the real-time approximation of the dynamical systems and to maintain the overall computational efficiency. The performance of this variable structure RBF network approximator with both Gaussian RBF (GRBF) and raised-cosine RBF (RCRBF) is analyzed. The compact support of RCRBF enables faster training and easier output evaluation of the network than that of the network with GRBF. The proposed real-time self-organizing RBF network approximator is then employed to approximate both linear and nonlinear dynamical systems to illustrate the effectiveness of our proposed approximation scheme, especially for higher order dynamical systems. The uniform ultimate boundedness of the approximation error is proved using the second method of Lyapunov.