Identification of nonlinear systems via piecewise general orthogonal polynomials operator

Based on a hybrid orthogonal function, a new linear, continuous and bounded operator - the piecewise general orthogonal polynomials operator (PGOPO) is proposed. Its main properties and operational rules have been strictly constructed based on the theory of mean-square convergence; these are useful to discuss the orthogonal polynomial approach in the proper mathematical framework. Then, applying the PGOPO method to solve the identification problem of nonlinear systems, a convergence analysis of the PGOPO approximation method has been given. Finally, using the PGOPO method to solve the parameter identification of two kinds of time-varying systems, simulation studies show that the algorithm is simpler and more effective than that of general orthogonal polynomials