Nonlinear system identification using wavelet networks

A novel identification scheme using wavelet networks is presented for nonli near dynamical systems. Based on fixed wavelet networks, parameter adaptati on laws are developed using a Lyapunov synthesis approach. This guarantees rite 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 multireso lution 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 system s. B-spline wavelets are used to form the wavelet networks and the identifi cation scheme is illustrated using a simulated example.