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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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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.
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Linear time-invariant Systems01:23

Linear time-invariant Systems

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Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit
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Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Published on: September 8, 2023

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Distributed Time-Varying Convex Optimization With Dynamic Quantization.

Ziqin Chen, Peng Yi, Li Li

    IEEE Transactions on Cybernetics
    |August 26, 2021
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    Summary
    This summary is machine-generated.

    This study introduces a distributed algorithm for optimizing networks with quantized communications. The method effectively reduces tracking errors, enabling systems to converge to optimal solutions despite data loss.

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    Area of Science:

    • Distributed Optimization
    • Networked Systems
    • Convex Optimization

    Background:

    • Agents in a network have individual time-varying objective functions.
    • Cooperative tracking of global time-varying optimal solutions is required.
    • Communication constraints, specifically quantized information, pose a challenge.

    Purpose of the Study:

    • To design a distributed algorithm for time-varying convex optimization over networks with quantized communications.
    • To minimize tracking errors caused by quantization in distributed optimization.
    • To ensure asymptotic tracking of optimal solutions even with information loss.

    Main Methods:

    • The algorithm is motivated by the alternating direction method of multipliers (ADMM).
    • A dynamic quantization scheme with a decaying scaling function is applied to reduce tracking error.
    • The tracking error is explicitly characterized concerning the limit of the decaying scaling function.

    Main Results:

    • The proposed algorithm effectively reduces tracking errors caused by quantized communications.
    • Theoretical analysis shows the algorithm can asymptotically track optimal solutions.
    • Convergence to optimal solutions is achieved even with information loss due to quantization.

    Conclusions:

    • The developed distributed algorithm is effective for time-varying convex optimization in networks with quantized communication.
    • The dynamic quantization scheme successfully mitigates the impact of information loss.
    • The findings are validated through numerical simulations, confirming the algorithm's practical applicability.