Adaptive tracking control for non-periodic reference signals under quantized observations

Abstract

This paper considers an adaptive tracking control problem for stochastic regression systems with multi-threshold quantized observations. Different from the existing studies for periodic reference signals, the reference signals in this paper are non-periodic. The main difficulty is how to ensure that the designed controller satisfies the uniformly bounded and excitation conditions that guarantee the convergence of the estimation in the controller under non-periodic reference signals. This paper designs two backward-shifted polynomials with time-varying parameters and a special projection structure, which break through periodic limitations and establish the convergence and tracking properties. To be specific, the adaptive tracking control law can achieve asymptotically optimal tracking for the non-periodic reference signal in the mean square sense. Besides, the proposed estimation algorithm is proved to converge to the true values in almost sure and mean square sense, and the convergence speed can reach $O\left(\frac{1}{k}\right)$ under suitable design of the quantized weight coefficients. Finally, the effectiveness of the proposed adaptive tracking control scheme is verified through a simulation.