未知多频系下一维不稳定热方程的自适应输出跟踪

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-07-21 DOI:10.1016/j.cnsns.2025.109142

Jun Chen , Junmin Wang , Xiufang Yu

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引用次数: 0

摘要

本文研究了一维非配位不稳定热方程的自适应输出跟踪问题。该系统受到有限维系外系统产生的干扰和参考信号的影响，这些干扰和参考信号具有多个未知的频率和幅度。通过构建辅助系统和内部模型动力学，重构了由可用状态组成的可测量跟踪误差。提出了一种自适应估计不确定参数的方法。设计了一种基于误差的自适应动态补偿器，采用反步法实现指数输出跟踪。数值算例说明了该策略的有效性。

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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Adaptive output tracking for 1-D unstable heat equations with unknown multi-frequency exosystem

In this paper, we address the adaptive output tracking problem for a 1-D unstable heat equation with non-collocated configurations. The system is subject to disturbances and reference signals generated by a finite-dimensional exosystem, which possess multiple unknown frequencies and amplitudes. By constructing an auxiliary system and internal model dynamics, we restructure the measurable tracking error composed of available states. An adaptive method is proposed to estimate the uncertain parameters. We design an error-based adaptive dynamic compensator to achieve exponential output tracking using the backstepping method. A numerical example is provided to illustrate the effectiveness of the proposed strategy.

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来源期刊

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.