Nonlinear system identification using Lyapunov based fully tuned dynamic RBF networks

This paper presents a stable, on-line identification scheme for multivariable nonlinear dynamic system. Growing Gaussian Radial Basis Function (GRBF) network with all its parameters being adaptable is used to approximate an unknown nonlinear system. Based on a continuous-time framework, the parameter adjustment law is derived using Lyapunov synthesis approach, which guarantees the stability of the overall system. In addition, to ensure the convergence of the approximation error, a growing strategy for the network is selected and a dead zone is incorporated in the tuning law. Simulation studies on identifying a time-varying nonlinear missile dynamics illustrate the superior performance of the proposed scheme. The studies also indicate that stability and reduction in approximation error can be extended to a network with pruning strategy, thereby resulting in a Growing and Pruning (GAP) RBF network, which can implement a more compact network structure.