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An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
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The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this...
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State Space Representation01:27

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The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
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State-space representation is a powerful tool for simulating physical systems on digital computers, necessitating the conversion of the transfer function into state-space form. Consider an nth-order linear differential equation with constant coefficients, like those encountered in an RLC circuit. The state variables are selected as the output and its n−1 derivatives. Differentiating these variables and substituting them back into the original equation produces the state equations.
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The conversion of state-space representation to a transfer function is a fundamental process in system analysis. It provides a method for transitioning from a time-domain description to a frequency-domain representation, which is crucial for simplifying the analysis and design of control systems.
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Finite-Horizon H∞ State Estimation for Complex Networks With Uncertain Couplings and Packet Losses: Handling

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    This study develops a state estimator for complex networks (CNs) facing uncertain couplings and packet loss. The method ensures performance constraints are met, offering a recursive algorithm for online state estimation.

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    Area of Science:

    • Control Systems Engineering
    • Network Science
    • Information Theory

    Background:

    • Complex networks (CNs) are susceptible to uncertainties in internal connections and data loss during transmission.
    • Effective state estimation is crucial for monitoring and controlling these networks, especially in the presence of communication constraints.

    Purpose of the Study:

    • To design a state estimator for complex networks (CNs) with uncertain inner couplings and packet losses.
    • To ensure a prescribed performance constraint is met for the dynamical error system over a finite horizon.
    • To develop a recursive algorithm for online computation of the state estimator.

    Main Methods:

    • Utilizing amplify-and-forward (AaF) relay protocols to enhance communication quality.
    • Modeling packet losses using Bernoulli random variables.
    • Deriving a sufficient condition for estimator existence and determining estimator gain via coupled backward Riccati difference equations (RDEs).

    Main Results:

    • A novel state estimator design for complex networks with uncertain parameters and communication noise.
    • A recursive algorithm suitable for real-time state estimation in networked systems.
    • Validation of the proposed method through a numerical example demonstrating its effectiveness.

    Conclusions:

    • The proposed state estimation method effectively addresses uncertainties and packet losses in complex networks.
    • The developed recursive algorithm facilitates practical online implementation for state estimation.
    • The findings contribute to robust control and monitoring of networked systems under challenging communication conditions.