论文标题
在统一持续激发下对二元价值系统的递归鉴定
Recursive Identification of Binary-Valued Systems under Uniform Persistent Excitations
论文作者
论文摘要
本文研究了具有统一的持续激发和观察噪声的设置值移动平均系统的面向控制的识别问题。提出了基于随机近似（基于SA的）算法，而没有投影或截断。该算法克服了现有的经验测量方法和递归投影方法的局限性，其中前者需要定期输入，后者需要投影以限制紧凑型集合中的搜索区域。分析算法的收敛性能，算法的收敛性，估计误差的分布尾声是通过促进的融合，可以通过一种融合来融合一项融合。基于此关键技术，基于SA的算法似乎是第一个达到$ o（\ sqrt {\ ln \ ln k/k}）$几乎确定的收敛速率的算法。同时，事实证明，均方根的收敛速度为$ O（1/k）$，即使在准确的观察下，这也是最好的。给出了一个数值示例，以证明所提出的算法和理论结果的有效性。
This paper studies the control-oriented identification problem of set-valued moving average systems with uniform persistent excitations and observation noises. A stochastic approximation-based (SA-based) algorithm without projections or truncations is proposed. The algorithm overcomes the limitations of the existing empirical measurement method and the recursive projection method, where the former requires periodic inputs, and the latter requires projections to restrict the search region in a compact set.To analyze the convergence property of the algorithm, the distribution tail of the estimation error is proved to be exponentially convergent through an auxiliary stochastic process. Based on this key technique, the SA-based algorithm appears to be the first to reach the almost sure convergence rate of $ O(\sqrt{\ln\ln k/k}) $ theoretically in the non-periodic input case. Meanwhile, the mean square convergence is proved to have a rate of $ O(1/k) $, which is the best one even under accurate observations. A numerical example is given to demonstrate the effectiveness of the proposed algorithm and theoretical results.
