  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.
