自动化学报2024,Vol.50Issue(2) :295-307.DOI:10.16383/j.aas.c221007

一类具有复杂执行器动态的双曲线型偏微分方程输出调节

Output Regulation for a Class of Hyperbolic PDEs With Complex Actuator Dynamics

肖宇 徐晓东 阳春华
自动化学报2024,Vol.50Issue(2) :295-307.DOI:10.16383/j.aas.c221007

一类具有复杂执行器动态的双曲线型偏微分方程输出调节

Output Regulation for a Class of Hyperbolic PDEs With Complex Actuator Dynamics

肖宇 1徐晓东 1阳春华1
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作者信息

  • 1. 中南大学自动化学院 长沙 410083
  • 折叠

摘要

本文研究了一类具有边界执行器动态特性的双曲线型偏微分方程(Partial differential equation,PDE)系统的输出调节问题.特别地,执行器由一组非线性常微分方程(Ordinary differential equation,ODE)描述,控制输入出现在执行器的一端而非直接作用在PDE系统上,这使得控制任务变得相当困难.基于几何设计方法和有限维与无限维反步法,本文提出了显式表达的输出调节器,实现了该类系统的扰动补偿及跟踪控制.并且我们采用Lyapunov稳定性理论严格证明了闭环系统及跟踪误差在范数意义上的指数稳定性.仿真实例对比验证了所提出控制方法的有效性.

Abstract

This paper investigates the output regulation problem for a class of hyperbolic partial differential equa-tion(PDE)systems with boundary actuator dynamics.Particularly,the control input appears at one end of the ac-tuator described by a set of ordinary differential equation(ODE)rather than directly in the PDE system,which makes the control task rather difficult.Based on the geometric design method as well as finite and infinite dimen-sional backstepping methods,an output regulator is explicitly provided in the paper so that the disturbance com-pensation and tracking control of this system are implemented.Moreover,we rigorously prove the exponential sta-bility of both the closed-loop system and the tracking error in the norm by employing the Lyapunov stability the-ory.The simulation example comparatively demonstrates the effectiveness of the proposed control method.

关键词

双曲线型偏微分方程/输出调节/执行器动态特性/非线性/反步法

Key words

Hyperbolic partial differential equation(PDE)/output regulation/actuator dynamics/nonlinearity/backstepping

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基金项目

国家重点研发项目(2022YFB3304700)

出版年

2024
自动化学报
中国自动化学会 中国科学院自动化研究所

自动化学报

CSTPCD北大核心
影响因子:1.762
ISSN:0254-4156
参考文献量29
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