On convergence of neural approximate nonlinear state estimators

The problem of designing a state observer for nonlinear systems has been faced in several works in the past decades and only recently researches focused on the discrete-time ones. In the paper, the case of a noisy measurement channel is addressed. By generalizing the classical least-squares method we compute the estimation law off-line by solving a functional optimization problem. Convergence results of the estimation error are stated and the approximate solution of the above problem is addressed by means of a feedforward neural network. A min-max technique is proposed to determine the weight coefficients of the “neural” observer so as to estimate the system state to any given degree of accuracy, thus guaranteeing the boundedness of the estimation error