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

TL;DR

This paper develops an adaptive tracking control method for stochastic systems with non-periodic signals and quantized observations, ensuring convergence and optimal tracking performance.

Contribution

It introduces a novel control scheme that overcomes periodicity limitations using backward-shifted polynomials and a special projection structure.

Findings

Achieves asymptotically optimal tracking for non-periodic signals

Proves convergence of estimation in almost sure and mean square senses

Convergence speed reaches O(1/k) under certain conditions

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 signal in this paper is non-periodic. Its 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 signal conditions. 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; 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 conditions. Finally, the effectiveness of the proposed adaptive tracking control scheme is verified through a simulation.