ADAPTIVE TRACKING OF A CLASS OF FIRST-ORDER SYSTEMS WITH BINARY-VALUED OBSERVATIONS AND FIXED THRESHOLDS

这份报纸为一阶的系统的一个班考虑适应追踪问题，珍视二进制代码的观察经由固定阀值产生了。一个递归的设计算法基于系统噪音的统计性质为参数评价被建议。然后，一条适应控制法律经由必然等价原则被设计。由关于估计的革新和输出预言的有条件的期望的使用，靠近环的系统被显示稳定、 asymptotically 最佳。同时，参数估计被证明肯定几乎是两个并且意味着平方会聚，并且评价错误的集中率也被获得。一个数字例子被给表明适应控制法律的效率。

This paper considers the adaptive tracking problem for a class of first-order systems with binary-valued observations generated via fixed thresholds. A recursive projection algorithm is proposed for parameter estimation based on the statistical properties of the system noise. Then, an adaptive control law is designed via the certainty equivalence principle. By use of the conditional expectations of the innovation and output prediction with respect to the estimates, the closed-loop system is shown to be stable and asymptotically optimal. Meanwhile, the parameter estimate is proved to be both almost surely and mean square convergent, and the convergence rate of the estimation error is also obtained. A numerical example is given to demonstrate the efficiency of the adaptive control law.