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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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。

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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

期刊介绍： The Journal is to provide an outlet for papers which are original and of high quality in mathematical control theory, systems theory, and applied information sciences. Short papers and mathematical correspondence or technical notes will be welcome, although the primary function of the journal is to publish papers of substantial length and coverage. The emphasis will be upon relevance, originality and clarify of presentation, although timeliness may well be an important feature in acceptable papers. Speculative papers that suggest new avenues for research or potential solutions to unsolved problems of control and information theory will be particularly welcome. Specific application papers will not normally be within the remit of the journal. Applications that illustrate techniques or theories will be acceptable. A prime function of the journal is to encourage the interplay between control and information theory and other mathematical sciences. All submitted papers will be judged on their merits by at least two referees and a full paper report will be available to the intending authors. Submitted articles will in general be published in an issue within six months of submission. Papers should not have previously published, nor should they be undes consideration for publication in another journal. This Journal takes publication ethics very seriously. If misconduct is found or suspected after the manuscript is published, the journal will investigate the matter and this may result in the article subsequently being retracted.