Adaptive Tracking Control of FIR Systems Under Binary-Valued Observations and Recursive Projection Identification

In this article, adaptive tracking control of finite impulse response (FIR) systems is studied with binary-valued measurements. An adaptive control strategy is proposed based on an online identification algorithm. First, the designed control inputs are proved to be bounded and satisfy a persistent excitation (PE) condition under the assumption of periodic and PE target signals, which ensures the convergence of the identification algorithm. Second, the convergence rate of the identification algorithm is proved to be $O(1/t)$ and it depends on the true parameter instead of a priori information of the parameter, which is more intuitive. Due to the convergence and the convergence rate of the identification algorithm, we finally prove that the adaptive tracking control is asymptotically optimal and the tracking speed is faster than the previous control algorithm. The simulations are given to validate the developed results in this article.