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首页> 外文期刊>International Journal of Control >Robust l{sub}1 estimation suing the Popov-Tsypkin multiplier with application to fault detection
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Robust l{sub}1 estimation suing the Popov-Tsypkin multiplier with application to fault detection

机译：使用Popov-Tsypkin乘法器进行鲁棒的l {sub} 1估计，并将其应用于故障检测

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This paper considers the design of robust l{sub}1 estimators based on multiplier theory (which is intimately related to mixed structured singular value theory) and the application of robust l{sub}1 estimators to robust fault detection. The key to estimator-based, robust fault detection is to generate residuals which are robust against plant uncertainties and external disturbance inputs, which in turn requires the design of robust estimators. Specifically, the Popov-Tsypkin multiplier is used to develop an upper bound on an l{sub}1 cost function over an uncertainty set. The robust l{sub}1 estimation problem is formulated as a parameter optimization problem in which the upper bound is minimized subject to a Riccati equation constraint. A continuation algorithm that uses quasi-Newton BFGS (the algorithm of Broyden, Fletcher, Goldfab and Shanno) corrections is developed to solves the minimization problem. The estimation algorithm has two stages. The first stage solves a mixed-norm H{sub}2/l{sub}1 estimation problem. In particular, it is initialized with a steady-state Kalman, filter and, by varying a design parameter from 0 to 1, the Kalman filter is deformed to an l{sub}1 estimator. In the second stage the l{sub}1 estimator is made robust. The robust l{sub}1 estimation framework is then applied to the robust fault detection of dynamic systems. The results are applied to a simplified longitudinal flight control system. It is shown that the robust fault detection procedure based on the robust l{sub}1 estimation methodology proposed in this paper can reduce false alarm rates.
机译：本文考虑了基于乘数理论（与混合结构奇异值理论密切相关）的鲁棒l {sub} 1估计器的设计，以及鲁棒l {sub} 1估计器在鲁棒故障检测中的应用。基于估计器的鲁棒故障检测的关键是生成对工厂不确定性和外部干扰输入具有鲁棒性的残差，这又需要设计鲁棒的估计器。具体而言，使用Popov-Tsypkin乘数来确定不确定集上1 {sub} 1成本函数的上限。健壮的1 {sub} 1估计问题被公式化为参数优化问题，其中上限受Riccati方程约束最小化。为解决最小化问题，开发了一种使用准牛顿BFGS校正的连续算法（Broyden，Fletcher，Goldfab和Shanno的算法）校正。估计算法分为两个阶段。第一阶段解决了混合范数H {sub} 2 / l {sub} 1估计问题。特别地，它用稳态卡尔曼滤波器初始化，并且通过将设计参数从0改变为1，卡尔曼滤波器变形为l {sub} 1估计器。在第二阶段，使l {sub} 1估计器健壮。然后将鲁棒的l {sub} 1估计框架应用于动态系统的鲁棒故障检测。将结果应用于简化的纵向飞行控制系统。结果表明，本文提出的基于鲁棒l {sub} 1估计方法的鲁棒故障检测程序可以降低误报率。

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