Adaptive tracking control under quantized observations and observation uncertainty with unbounded variance

In this paper, we present a matrix-type adaptive tracking control scheme for a stochastic regression system with multi-threshold quantized observations and observation uncertainty. This observation uncertainty is described by an additive random noise, whose variance could be a polynomial-type rate of increase and tends to infinity. Our method, first, to handle simultaneously parameter uncertainty, quantized observation, and observation uncertainty, incorporates an online stochastic approximation-type parameter identification algorithm. Second, based on the above identification algorithm, we construct a matrix-type adaptive tracking control law by the certainty equivalence principle. In addition, under suitable conditions, the above identification algorithm and matrix-type adaptive tracking control law in the mean square sense can ensure that the estimations of the unknown parameters converge to the true values and achieve asymptotically optimal tracking of the periodic reference signal, respectively. To characterize the effect of observation uncertainty on the convergence speed of the identification algorithm in the mean square sense, a quantitative relationship between observation uncertainty and the convergence speed is proposed. Finally, the effectiveness of the proposed matrix-type adaptive tracking control scheme is verified through a simulation.