Delayed boundary control of a heat equation under discrete-time point measurements

Selivanov, Anton; Fridman, Emilia

doi:10.1109/cdc.2017.8263827

Cited by 3 publications

(3 citation statements)

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“…we have α 1 + α 2 + α 3 ≤ 1. Clearly, Lemma 5 remains true for α 1 + α 2 + α 3 ≤ 1 implying (11). Each rectangle cornered at x i ∈ supp c i and lying in Ω i (see Fig.…”

Section: Pointlike Observer For a 2d Heat Equationmentioning

confidence: 94%

“…For 1D heat equations, point observers/controllers have been constructed and analyzed under continuous [5], [6], [7], [8], [9], [10] and sampled in time [7], [11] measurements. N -D diffusion equations with averaged measurements (i.e., the state values are averaged over subdomains covering the entire space domain) have been studied in [12], [13], [14].…”

Section: Introductionmentioning

confidence: 99%

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Sampled-data H∞ filtering of a 2D heat equation under pointlike measurements

Selivanov

Fridman

2018

2018 IEEE Conference on Decision and Control (CDC)

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“…we have α 1 + α 2 + α 3 ≤ 1. Clearly, Lemma 5 remains true for α 1 + α 2 + α 3 ≤ 1 implying (11). Each rectangle cornered at x i ∈ supp c i and lying in Ω i (see Fig.…”

Section: Pointlike Observer For a 2d Heat Equationmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

Sampled-data H∞ filtering of a 2D heat equation under pointlike measurements

Selivanov

Fridman

2018

2018 IEEE Conference on Decision and Control (CDC)

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“…We show that both the boundary control and the point control with large enough number of actuations guarantee the exponential stability of the closed-loop system with an arbitrary decay rate smaller than that of the observer's estimation error. Preliminary results on the boundary control have been published in [43].…”

Section: Introductionmentioning

confidence: 99%

Delayed point control of a reaction–diffusion PDE under discrete-time point measurements

Selivanov

Fridman

2018

Automatica

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We consider stabilization problem for reaction-diffusion PDEs with point actuations subject to a known constant delay. The point measurements are sampled in time and transmitted through a communication network with a time-varying delay. To compensate the input delay, we construct an observer for the future value of the state. Using a time-varying observer gain, we ensure that the estimation error vanishes exponentially with a desired decay rate if the delays and sampling intervals are small enough while the number of sensors is large enough. The convergence conditions are obtained using a Lyapunov-Krasovskii functional, which leads to linear matrix inequalities (LMIs). We design output-feedback point controllers in the presence of input delays using the above observer. The boundary controller is constructed using the backstepping transformation, which leads to a target system containing the exponentially decaying estimation error. The in-domain point controller is designed and analysed using an improved Wirtingerbased inequality. We show that both controllers can guarantee the exponential stability of the closed-loop system with an arbitrary decay rate smaller than that of the observer's estimation error.

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Backstepping and Sequential Predictors for Control Systems

Weston¹

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Delayed boundary control of a heat equation under discrete-time point measurements

Abstract: This is a repository copy of Delayed boundary control of a heat equation under discrete-time point measurements.

Cited by 3 publications

References 42 publications

Sampled-data H∞ filtering of a 2D heat equation under pointlike measurements

Sampled-data H∞ filtering of a 2D heat equation under pointlike measurements

Delayed point control of a reaction–diffusion PDE under discrete-time point measurements

Backstepping and Sequential Predictors for Control Systems

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