Definition and Analytical Expression on State Observe Ability for Linear Discrete-time Systems with the Bounded Noise Energy
In this article, the definition on the observe ability and its relation to the signal detecting performance are studied systematically for the linear discrete-time(LDT) systems. Firstly, to define and analyze the observe ability for the practical systems with the measured noise, six kinds of bounded noise models are classified. For the noise energy bounded case, the observability ellipsoid and the image observability ellipsoid are defined by the state observed error and then a novel concept on the LDT systems, called as the observe ability, is proposed. Based on that, some theorems and properties about the observe ability and the signal detecting performances are given and proven, and then the reason that to maximize the observe ability is to optimize the signal detecting performances is established. Secondly, a dual relation between the observability ellipsoid and the controllability ellipsoid, which volumes and radii are respectively with some inverse relations, is stated and proven. Accordingly, the analytical computing equations for the volume of the two observability ellipsoids are got and some analytical shape factors of these ellipsoids are deconstructed. Based on these effective compting for the volumes, radii, and shape factors, analyzing and optimizing for the observe ability can be carried out. Thirdly, to compare rationally the state observe ability between the different systems or different system parameters, the normalization of the output variables, the state variables, and the system models are discussed. Finally, some numerical experiments and their results show the effectiveness of the computing and comparing methods for the observe ability.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Secrecy Outage Analysis Over Fluctuating Two-Ray Fading Channels
In this letter, we analyze the secrecy outage probability (SOP) over fluctuating two-ray fading channels but with a different definition from the one adopted in [5]. Following the new defined SOP, we derive an analytical…
validVocal Bursts Valence PredictionFinite Expression Methods for Discovering Physical Laws from Data
Nonlinear dynamics is a pervasive phenomenon observed in scientific and engineering disciplines. However, the task of deriving analytical expressions to describe nonlinear dynamics from limited data remains challenging. …
A Debiased MDI Feature Importance Measure for Random Forests
Tree ensembles such as Random Forests have achieved impressive empirical success across a wide variety of applications. To understand how these models make predictions, people routinely turn to feature importance measure…
Feature Importancefeature selectionSelection biasAnalytical Expression and Deconstruction of the Volume of the Controllability Ellipsoid
In this article, we present three theorems and develop an effective analytical method to compute analytically the volume of the controllability ellipsoid for the linear discrete-time (LDT) systems with $n$ different eige…
Symbolic Regression for PDEs using Pruned Differentiable Programs
Physics-informed Neural Networks (PINNs) have been widely used to obtain accurate neural surrogates for a system of Partial Differential Equations (PDE). One of the major limitations of PINNs is that the neural solutions…
regressionSymbolic Regression