On a new method for the state and output feedback exponential stabilization of a cascaded wave PDE-ODE system with nonlinear boundary condition

IF 1.6 4区计算机科学 Q3 AUTOMATION & CONTROL SYSTEMS

IMA Journal of Mathematical Control and Information Pub Date : 2023-10-26 DOI:10.1093/imamci/dnad027

Najmeh Ghaderi

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引用次数: 0

Abstract

Abstract This study presents a novel approach for the state and output feedback exponential control of cascaded unstable ODE-wave equations with nonlinear boundary condition. The new approach can be also used to investigate the state and output feedback stabilization of other cascaded ODE-partial differential equation (PDE) systems with nonlinear boundary condition. The interconnection between the ODE and wave PDE with the nonlinear boundary is bi-directional at two points. First, an exponential controller is planned and the well-posed and exponential stability of the closed-loop system is derived. Next, an exponential observer is designed, whereby the exponential stability of the overall error system is shown. Then, an observer-based output feedback control that causes the overall real system to be exponentially stable is built. The existence and exponential stability of the solution to the overall closed-loop system are further deduced. Finally, simulation results are given to verify the effectiveness, feasibility and validity of the proposed technique.

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基于非线性边界条件的级联波PDE-ODE系统状态和输出反馈指数镇定新方法

提出了一种具有非线性边界条件的级联不稳定ode波动方程状态和输出反馈指数控制的新方法。该方法也可用于研究其他具有非线性边界条件的级联ode -偏微分方程(PDE)系统的状态和输出反馈镇定。具有非线性边界的微分方程和波微分方程在两点上是双向互连。首先，规划了一个指数控制器，并推导了闭环系统的适定稳定性和指数稳定性。其次，设计了一个指数观测器，从而显示了整个误差系统的指数稳定性。然后，建立了一个基于观测器的输出反馈控制，使整个实际系统呈指数稳定。进一步推导了整个闭环系统解的存在性和指数稳定性。最后给出了仿真结果，验证了所提技术的有效性、可行性和有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

IMA Journal of Mathematical Control and Information 工程技术-应用数学

CiteScore

3.30

自引率

6.70%

发文量

审稿时长

>12 weeks

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