Analysis of a Class of Adaptive Robustified Predictors in the Presence of Noise Uncertainty

Original scientific paper A new class of adaptive robust predictors has been considered in the paper. First an optimal predictor is developed, based on the minimization of a generalized mean square prediction error criterion. Starting from the obtained result, an adaptive robust predictor is synthesized through minimization of a modified criterion in which a suitably chosen non-linear function of the prediction error is introduced instead of the quadratic one. Unknown parameters of the predictor are estimated at each step by applying a recursive algorithm of stochastic gradient type. The convergence of the proposed adaptive robustified prediction algorithm is established theoretically using the Martingale theory. It has been shown that the proposed adaptive robust prediction algorithm converges to the optimal systems output prediction. The feasibility of the proposed approach is demonstrated by solving a practical problem of designing a robust version of adaptive minimum variance controller.