Delayed finite-dimensional observer-based control of 1-D parabolic PDEs

被引:28
|
作者
Katz, Rami [1 ]
Fridman, Emilia [1 ]
机构
[1] Tel Aviv Univ, Sch Elect Engn, Tel Aviv, Israel
基金
以色列科学基金会;
关键词
Distributed parameter systems; Heat equation; Observer-based control; Time-delay; Lyapunov method;
D O I
10.1016/j.automatica.2020.109364
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
In our recent paper a constructive method for finite-dimensional observer-based control of 1-D linear heat equation was suggested. In the present paper we aim to extend this method to the case of input/output general time-varying delays or sawtooth delays (that correspond to network-based control). We assume known measurement delays and, for the first time under observer-based control of PDEs, unknown input delays. We use a modal decomposition approach, and consider boundary or non-local sensing together with non-local actuation, or Dirichlet actuation with non-local sensing. The dimension of the controller is equal to the number of unstable modes, whereas the observer may have a larger dimension N. Under the Dirichlet actuation we present two methods: a direct one that manages with time-varying input and output delays, and a dynamic-extension-based one that treats constant input and time-varying output delays. To compensate the fast-varying output delay (without any constraints on the delay derivative) that appears in the infinite-dimensional part of the closed-loop system, we combine Lyapunov functionals with Halanay's inequality. For the slowly-varying output delay (with the delay derivative smaller than d < 1), we suggest a direct Lyapunov method. We provide LMIs for finding N and upper bounds on the delays that preserve the exponential stability. (c) 2020 Elsevier Ltd. All rights reserved.
引用
收藏
页数:9
相关论文
共 50 条
  • [31] Constrained control of 1-D parabolic PDEs using sampled in space sensing and actuation
    Kang, Wen
    Fridman, Emilia
    [J]. SYSTEMS & CONTROL LETTERS, 2020, 140 (140)
  • [32] Global finite-dimensional observer-based stabilization of a semilinear heat equation with large input delay
    Katz, Rami
    Fridman, Emilia
    [J]. SYSTEMS & CONTROL LETTERS, 2022, 165
  • [33] DECAY ESTIMATES FOR 1-D PARABOLIC PDES WITH BOUNDARY DISTURBANCES
    Karafyllis, Iasson
    Krstic, Miroslav
    [J]. ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2018, 24 (04) : 1511 - 1540
  • [34] ISS with Respect to Boundary Disturbances for 1-D Parabolic PDEs
    Karafyllis, Iasson
    Krstic, Miroslav
    [J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2016, 61 (12) : 3712 - 3724
  • [35] Active Disturbance Rejection Control and Disturbance Observer-Based Control Approach to 1-d Flexible String System
    Zhai, Yin-Guang
    Zhou, Hua-Cheng
    [J]. 2021 PROCEEDINGS OF THE 40TH CHINESE CONTROL CONFERENCE (CCC), 2021, : 855 - 860
  • [36] Finite-Dimensional Hybrid Observer for Delayed Impulsive Model of Testosterone Regulation
    Yamalova, Diana
    Churilov, Alexander
    Medvedev, Alexander
    [J]. MATHEMATICAL PROBLEMS IN ENGINEERING, 2015, 2015
  • [37] Observer-Based Periodic Event-Triggered and Self-Triggered Boundary Control of a Class of Parabolic PDEs
    Rathnayake, Bhathiya
    Diagne, Mamadou
    [J]. IEEE Transactions on Automatic Control, 2024, 69 (12) : 8836 - 8843
  • [38] Observer-based finite-time control of time-delayed jump systems
    He, Shuping
    Liu, Fei
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 2010, 217 (06) : 2327 - 2338
  • [39] Delayed observer-based H∞ control for networked control systems
    Liu, Lijia
    Liu, Xianli
    Man, Chuntao
    Xu, Chengyang
    [J]. NEUROCOMPUTING, 2016, 179 : 101 - 109
  • [40] Sampled-data finite-dimensional boundary control of 1D parabolic PDEs under point measurement via a novel ISS Halanay's inequality
    Katz, Rami
    Fridman, Emilia
    [J]. AUTOMATICA, 2022, 135