Nonlinear system identification using wavelet networks

A novel identification scheme using wavelet networks is presented for nonlinear dynamical systems. Based on fixed wavelet networks, parameter adaptation laws are developed using a Lyapunov synthesis approach. This guarantees the stability of the overall identification scheme and the convergence of both the parameters and the state errors, even in the presence of modelling errors. Using the decomposition and reconstruction techniques of multiresolution decompositions, variable wavelet networks are introduced to achieve a desired estimation accuracy and a suitable sized network, and to adapt to variations of the characteristics and operating points in nonlinear systems. B-spline wavelets are used to form the wavelet networks and the identification scheme is illustrated using a simulated example.