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.
机构:
St Petersburg State Univ, Fac Math & Mech, St Petersburg 198504, Russia
Uppsala Univ, Informat Technol, S-75105 Uppsala, SwedenSt Petersburg State Univ, Fac Math & Mech, St Petersburg 198504, Russia
Yamalova, Diana
Churilov, Alexander
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St Petersburg State Univ, Fac Math & Mech, St Petersburg 198504, RussiaSt Petersburg State Univ, Fac Math & Mech, St Petersburg 198504, Russia
Churilov, Alexander
Medvedev, Alexander
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Uppsala Univ, Informat Technol, S-75105 Uppsala, SwedenSt Petersburg State Univ, Fac Math & Mech, St Petersburg 198504, Russia
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Department of Electrical and Computer Engineering, University of California San Diego, 9500 Gilman Dr, La Jolla, CADepartment of Electrical and Computer Engineering, University of California San Diego, 9500 Gilman Dr, La Jolla, CA
Rathnayake B.
Diagne M.
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Department of Mechanical and Aerospace Engineering, University of California San Diego, 9500 Gilman Dr, La Jolla, CADepartment of Electrical and Computer Engineering, University of California San Diego, 9500 Gilman Dr, La Jolla, CA