On Strong Consistency of a Class of Recursive Stochastic Newton-Raphson Type Algorithms with Application to Robust Linear Dynamic System Identification

The recursive stochastic algorithms for estimating the parameters of linear discrete-time dynamic systems in the presence of disturbance uncertainty has been considered in the paper. Problems related to the construction of min-max optimal recursive algorithms are demonstrated. In addition, the robustness of the proposed algorithms has been addressed. Since the min-max optimal solution cannot be achieved in practice, an approximate optimal solution based on a recursive stochastic NewtonRaphson type procedure is suggested. The convergence of the proposed practically applicable robustified recursive algorithm is established theoretically using the martingale theory. Both theoretical and experimental analysis related to the practical robustness of the proposed algorithm are also included.