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Linear time-invariant Systems01:23

Linear time-invariant Systems

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A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
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System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
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Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
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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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Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
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In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
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Encoding-decoding strategy based resilient state estimation for bias-corrupted stochastic nonlinear systems.

Jiahui Li1, Hongli Dong1, Yuxuan Shen1

  • 1Artificial Intelligence Energy Research Institute, Northeast Petroleum University, Daqing 163318, China; Heilongjiang Provincial Key Laboratory of Networking and Intelligent Control, Northeast Petroleum University, Daqing 163318, China; SANYA Offshore Oil & Gas Research Institute, Northeast Petroleum University, Sanya 572024, China.

ISA Transactions
|May 31, 2022
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Summary
This summary is machine-generated.

This study introduces a resilient state estimation scheme for stochastic nonlinear systems using a binary encoding strategy (BES) to improve data robustness against channel noise. The method ensures bounded estimation errors, enhancing system reliability.

Keywords:
Binary encoding strategyBit errorDynamical biasResilient state estimator

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Area of Science:

  • Control Systems Engineering
  • Information Theory
  • Stochastic Systems

Background:

  • State estimation for stochastic nonlinear systems is challenging due to inherent uncertainties and potential dynamical biases.
  • Data transmission over noisy channels, like the binary symmetric channel (BSC), can introduce bit errors, compromising estimation accuracy.
  • Existing methods may not adequately address both system dynamics and channel impairments simultaneously.

Purpose of the Study:

  • To develop a novel resilient state estimation scheme for stochastic nonlinear systems.
  • To enhance data robustness against random bit errors introduced by a binary symmetric channel (BSC) using a binary encoding strategy (BES).
  • To ensure the estimation error dynamics are exponentially ultimately bounded in the mean square.

Main Methods:

  • Utilizing a binary encoding strategy (BES) to encode system states for transmission over a memoryless binary symmetric channel (BSC).
  • Modeling bit errors using Bernoulli distributed random variables to characterize channel noise effects.
  • Employing a resilient state estimator designed to handle potential gain fluctuations and ensure robust performance.
  • Formulating the problem to guarantee exponential ultimate boundedness of the estimation error in the mean square.

Main Results:

  • A sufficient criterion for the existence of the proposed resilient estimator was derived.
  • The parameters for the resilient estimator were obtained by solving a convex optimization problem.
  • The proposed scheme effectively bounds the estimation error dynamics in the mean square, demonstrating resilience against channel noise and system uncertainties.

Conclusions:

  • The novel resilient estimation scheme effectively addresses state estimation in stochastic nonlinear systems with dynamical bias and channel noise.
  • The developed method provides a robust approach for maintaining estimation accuracy under challenging communication conditions.
  • The theoretical results are validated through an illustrative simulation example, confirming the scheme's practical applicability.