Robust Finite-time Stabilization of Linear Systems with Limited State Quantization

Alapfogalmak

Designing a finite-time stabilizer for linear systems with limited state quantization using generalized homogeneity.

Kivonat

This paper explores the robust asymptotic stabilization of linear systems with limited state quantization. It introduces a novel approach based on generalized homogeneity, utilizing a homogeneous spherical quantizer. The design is supported by theoretical results and numerical simulations. The content is structured as follows:

Introduction to quantization in control systems.
Problem formulation for finite-time stabilization.
Preliminary concepts on homogeneity and homogeneous functions.
Main results on the design of a homogeneous spherical quantizer.
Numerical example validating the proposed approach.
Conclusion highlighting the potential for future research.

Statisztikák

A = [0 2 3]
B = [0; 0; 1.5]
Gd = [3 -0.75 0; 0 2 0; 0 1 0]
P = [0.0053 0.0037 0.0185; 0.0037 0.0212 0.0381; 0.0185 0.0381 0.2522]
K = [-0.1327 0.4089 1.7270]

Idézetek

"Quantization is an important process of networked control system design aimed at the reduction of data transmission."
"A linear feedback with finite static state quantizer can only ensure practical stability of LTI system."
"The proposed quantized stabilizer rejects some classes of additive non-vanishing perturbations."

Főbb Kivonatok

Robust Finite-time Stabilization of Linear Systems with Limited State Quantization

by Yu Zhou,Andr... : arxiv.org 03-27-2024

https://arxiv.org/pdf/2403.17184.pdf

Mélyebb kérdések

How can the proposed homogeneous spherical quantizer be optimized for reduced chattering phenomenon?

The chattering phenomenon in the control input can be reduced in the proposed homogeneous spherical quantizer by implementing techniques to smooth out the discontinuities that lead to chattering. One approach is to introduce hysteresis in the quantization process, which can help reduce rapid switching between quantization levels. By incorporating a deadband or a small range of values around the quantization thresholds, the system can avoid frequent transitions that cause chattering. Additionally, using a more sophisticated quantization algorithm that considers the rate of change of the signal can help in reducing chattering. By dynamically adjusting the quantization levels based on the signal dynamics, the system can achieve smoother control inputs and minimize chattering effects.

What are the implications of limited data transmission on the stability of the closed-loop system?

Limited data transmission can have significant implications on the stability of the closed-loop system, especially when using quantized feedback control. The key implications include:

Increased Quantization Error: Limited data transmission can lead to higher quantization errors, as the number of quantization levels is restricted. This increased quantization error can affect the performance of the control system and may lead to instability if not properly addressed.

Chattering Phenomenon: Limited data transmission can exacerbate the chattering phenomenon in the control system. The discrete nature of quantization combined with limited data can result in rapid and frequent switching between quantization levels, leading to chattering in the control input.

Stability Margin Reduction: Limited data transmission can reduce the stability margin of the closed-loop system. With fewer quantization levels available, the system may become more sensitive to disturbances and uncertainties, potentially compromising stability.

Control Performance Degradation: Limited data transmission can impact the control performance of the system by introducing delays, packet losses, or data corruption. These factors can affect the accuracy of the control input and the system's ability to track reference signals, leading to degraded performance.

How does the concept of generalized homogeneity impact the design of control systems beyond linear systems with quantization?

The concept of generalized homogeneity has broader implications for control system design beyond linear systems with quantization. Some key impacts include:

Nonlinear Systems: Generalized homogeneity can be applied to nonlinear systems to design controllers that exhibit homogeneity properties. By leveraging the symmetry of homogeneity, controllers can be designed to achieve stability, convergence, and robustness in nonlinear systems.

Robust Control: Generalized homogeneity can enhance the robustness of control systems by providing a framework for designing controllers that are resilient to uncertainties, disturbances, and variations in system parameters. Homogeneous controllers can offer robust performance guarantees in the presence of disturbances.

Adaptive Control: The concept of generalized homogeneity can be integrated into adaptive control strategies to facilitate adaptive tuning of controller parameters based on the system's dynamics. By incorporating homogeneity principles, adaptive controllers can adapt to varying operating conditions and maintain stability.

Networked Control Systems: In the context of networked control systems, generalized homogeneity can be utilized to design controllers that are robust to communication constraints, delays, and packet losses. Homogeneous control laws can help mitigate the effects of limited data transmission on system stability and performance.

Overall, the concept of generalized homogeneity provides a powerful framework for designing advanced control systems that exhibit desirable properties such as stability, robustness, and adaptability across a wide range of system dynamics and control challenges.