The filtering-based recursive least squares identification and convergence analysis for nonlinear feedback control systems with coloured noises

The coloured noise is ubiquitous in industrial processes. This paper addresses the identification problem for the nonlinear feedback systems with coloured noise. Firstly, a direct identification scheme based on the least squares principle is developed to estimate the whole parameters of the nonlinear feedback systems and the convergence analysis is carried out through the stochastic stability theory. Secondly, for the purpose of improving the estimation accuracy, a filtering-based identification framework is proposed by constructing a linear filter for filtering the input data, output data and the coloured noise, and the coloured noise is transformed into a white noise. This identification scheme based on the filtering technique can effectively reduce the adverse effects caused by coloured noise and parameter estimation accuracy is enhanced compared with the direct least squares algorithm. Meanwhile, the convergence analysis of the filtering-based identification algorithm is given to provide a theoretical analysis. Finally, the simulation example is carried out by performance test and comparison analysis and simulation results show the effectiveness of the proposed identification methods.