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Related Concept Videos

Sampling Continuous Time Signal01:11

Sampling Continuous Time Signal

251
In signal processing, a continuous-time signal can be sampled using an impulse-train sampling technique, followed by the zero-order hold method. Impulse-train sampling involves the use of a periodic impulse train, which consists of a series of delta functions spaced at regular intervals determined by the sampling period. When a continuous-time signal is multiplied by this impulse train, it generates impulses with amplitudes corresponding to the signal's values at the sampling points.
In the...
251
Sampling Theorem01:15

Sampling Theorem

340
In signal processing, the analysis of continuous-time signals, denoted as x(t), often involves sampling techniques to convert these signals into discrete-time signals. This process is essential for digital representation and manipulation. A critical component in sampling is the train of impulses, characterized by the sampling interval and the sampling frequency. The relationship between these parameters and the original signal's properties dictates the success of the sampling process.
340
State Space Representation01:27

State Space Representation

208
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.
Consider an RLC circuit, a...
208
Basic Discrete Time Signals01:16

Basic Discrete Time Signals

204
The unit step sequence is defined as 1 for zero and positive values of the integer n. This sequence can be graphically displayed using a set of eight sample points, showing a step function starting from n=0 and remaining constant thereafter.
The unit impulse or sample sequence is mathematically expressed as zero for all n values except at n=0, where it is one. The unit impulse sequence, denoted by δ(n), is the first difference of the unit step sequence, while the unit step sequence u(n) is...
204
Upsampling01:22

Upsampling

237
Managing signal sampling rates is essential in digital signal processing to maintain signal integrity. A decimated signal, characterized by a reduced frequency range due to its lower sampling rate, can be upsampled by inserting zeros between each sample. This upsampling process expands the original spectrum and introduces repeated spectral replicas at intervals dictated by the new Nyquist frequency. To refine this zero-inserted sequence, it is passed through a lowpass filter with a cutoff...
237
Transfer Function to State Space01:23

Transfer Function to State Space

259
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.
In an...
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A Method for Tracking the Time Evolution of Steady-State Evoked Potentials
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Sampled-Data State Estimation for LSTM.

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    Summary
    This summary is machine-generated.

    This study presents a novel state estimator for continuous-time long short-term memory (LSTM) neural networks with irregular data sampling. The method models LSTMs as parameter-varying systems, enabling robust state estimation for applications like robot control.

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    Area of Science:

    • Control Systems Engineering
    • Artificial Intelligence
    • Machine Learning

    Background:

    • Continuous-time Long Short-Term Memory (LSTM) neural networks are powerful tools for sequence modeling but pose challenges for state estimation due to irregularly sampled outputs.
    • Existing state estimation methods often struggle with the dynamic, parameter-varying nature of LSTM gate units and non-uniform data acquisition.
    • Accurate state estimation is crucial for understanding and controlling complex dynamic systems, including those driven by neural networks.

    Purpose of the Study:

    • To develop a sampled-data state estimator design method for continuous-time LSTM neural networks with irregularly sampled output data.
    • To model the LSTM neural network as a continuous-time linear parameter-varying (LPV) system dependent on its gate units.
    • To demonstrate the practical applicability of the proposed state estimation method in a robotics context.

    Main Methods:

    • The LSTM structure is analyzed to derive its dynamic equation, enabling its representation as a continuous-time LPV system.
    • Sampled-data Luenberger- and Arcak-type state estimator design methods are formulated using linear matrix inequalities (LMIs).
    • The design leverages the specific properties of LSTM gate units to ensure effective state estimation.

    Main Results:

    • A novel sampled-data state estimator for continuous-time LSTMs with irregular outputs was successfully designed.
    • The proposed method models LSTMs as LPV systems, facilitating the application of established control design techniques.
    • A numerical example confirmed the absolute stability analysis, and a practical demonstration with a robot manipulator's behavior generation model validated the approach.

    Conclusions:

    • The developed state estimator provides an effective solution for estimating the states of continuous-time LSTMs with irregularly sampled data.
    • The LPV system modeling approach offers a robust framework for designing state estimators for complex neural network architectures.
    • The method shows significant promise for real-world applications, particularly in robotics and control systems requiring accurate state feedback.