We consider the design of functional estimators, i.e., approaches to compute an estimate of a nonlinear function of the state of a general nonlinear dynamical system subject to process noise based on noisy output measurements. To this end, we introduce a novel functional detectability notion in the form of incremental input/output-to-output stability (δ-IOOS). We show that δ-IOOS is a necessary condition for the existence of a functional estimator satisfying an input-to-output type stability property. Additionally, we prove that a system is functional detectable if and only if it admits a corresponding δ-IOOS Lyapunov function. Furthermore, δ-IOOS is shown to be a sufficient condition for the design of a stable functional estimator by introducing the design of a full information estimation (FIE) approach for functional estimation. Together, we present a unified framework to study functional estimation with a detectability condition, which is necessary and sufficient for the existence of a stable functional estimator, and a corresponding functional estimator design. The practical need for and applicability of the proposed functional estimator design is illustrated with a numerical example of a power system.

中文翻译：

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非线性功能估计：功能可检测性和全信息估计


我们考虑了函数估计器的设计，即基于噪声输出测量计算受过程噪声影响的一般非线性动力学系统状态的非线性函数估计的方法。为此，我们以增量输入/输出到输出稳定性 （δ-IOOS） 的形式引入了一种新的功能可检测性概念。我们表明，δ-IOOS 是满足输入到输出类型稳定性特性的函数估计器存在的必要条件。此外，我们证明当且仅当系统允许相应的 δ-IOOS Lyapunov 函数时，系统才是功能可检测的。此外，通过引入全信息估计 （FIE） 方法的设计，δ-IOOS 被证明是设计稳定功能估计器的充分条件。总之，我们提出了一个统一的框架来研究具有可检测性条件的功能估计，这对于稳定的功能估计器和相应的功能估计器设计是必要和充分的。通过电力系统的数值示例说明了所提出的功能估计器设计的实际需求和适用性。