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Generalized set-theoretic interval observer using element-wise nonnegativity transformation
Automatica ( IF 6.4 ) Pub Date : 2021-01-16 , DOI: 10.1016/j.automatica.2020.109452
Feng Xu

This paper proposes a generalized set-theoretic interval observer (GSIO) for robust state estimation of discrete linear time-invariant (LTI) systems with bounded uncertainties. Including the previous set-theoretic interval observer (SIO) as a special case, the proposed GSIO only requires to transform the system matrix of the first subsystem to be nonnegative. Based on this idea, a nonsmooth H optimization method is used to design a nonnegative subsystem matrix for the first subsystem based on an element-wise nonnegativity transformation. The advantage of this method is that it can design a nonnegative subsystem matrix by transforming each of its elements to be nonnegative, which does not impact any structural constraints on matrix elements. This implies that more extra design degrees of freedom could be obtained from the coordinate transformation and observer gain matrices, which can optimize state estimation performance of GSIO (e.g., suppress the effects of disturbances and noises). In this way, we could not only achieve an expected balance between robust state estimation conservatism and computational complexity but also better robust state estimation performance. Besides, under the framework of the proposed GSIO, this paper further proves its existence, gives its stability condition and compares it with the set-valued observer (SVO) and the interval observer (IO) in state estimation conservatism, which together forms a complete theoretic system for the proposed GSIO. At the end of this paper, numerical examples are used to illustrate the effectiveness of the GSIO.



中文翻译:

使用逐元素非负变换的广义集合理论间隔观测器

本文提出了一种广义集理论间隔观测器(GSIO),用于具有不确定性的离散线性时不变(LTI)系统的鲁棒状态估计。包括以前的集合理论间隔观测器(SIO)作为特殊情况,建议的GSIO仅需要将第一个子系统的系统矩阵转换为非负数。根据这个想法,H优化方法用于基于元素非负性转换为第一个子系统设计一个非负子系统矩阵。此方法的优点是,可以通过将其每个元素转换为非负数来设计非负子系统矩阵,这不会影响矩阵元素的任何结构约束。这意味着可以从坐标变换和观察者增益矩阵获得更多的额外设计自由度,这可以优化GSIO的状态估计性能(例如,抑制干扰和噪声的影响)。这样,我们不仅可以在鲁棒状态估计的保守性和计算复杂性之间达到预期的平衡,而且还可以获得更好的鲁棒状态估计性能。此外,在拟议的GSIO框架下,本文进一步证明了它的存在,给出了它的稳定性条件,并将其与状态估计保守性上的集值观测器(SVO)和区间观测器(IO)进行了比较,它们共同构成了所提出的GSIO的完整理论体系。在本文的最后,通过数字示例说明了GSIO的有效性。

更新日期:2021-01-18
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