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

Selivanov, Anton; Fridman, Emilia

doi:10.1109/cdc.2018.8619284

Cited by 6 publications

(5 citation statements)

References 20 publications

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“…(81) below). However, this issue has been overcome in [183] by considering pointlike measurements for 2D heat equations presented in the next subsection.…”

Section: Point Measurementsmentioning

confidence: 99%

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Survey on time-delay approach to networked control

Liu

Selivanov

Fridman

2019

Annual Reviews in Control

Self Cite

131

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This paper provides a survey on time-delay approach to networked control systems (NCSs). The survey begins from a brief summary on fundamental network-induced issues in NCSs and the main approaches to the modelling of NCSs. In particular, a comprehensive introduction to time-delay approach to sampled-data and networked control is provided. Then, recent results on time-delay approach to event-triggered control are recalled. The survey highlights time-delay approach developed to modelling, analysis and synthesis of NCSs, under communication constraints, with a particular focus on Round-Robin, Try-once-discard and stochastic protocols. The time-delay approach allows communication delays to be larger than the sampling intervals in the presence of scheduling protocols. Moreover, some results on networked control of distributed parameter systems are surveyed. Finally, conclusions and some future research directions are briefly addressed.

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“…(81) below). However, this issue has been overcome in [183] by considering pointlike measurements for 2D heat equations presented in the next subsection.…”

Section: Point Measurementsmentioning

confidence: 99%

“…Moreover, if ε from (75) gets smaller (i.e., max i c i L∞ gets bigger), then the maximum allowable sampling h decreases. The LMI-based convergence conditions combining the above ideas can be found in [183].…”

Section: Pointlike Measurements For 2d Domainsmentioning

confidence: 99%

Survey on time-delay approach to networked control

Liu

Selivanov

Fridman

2019

Annual Reviews in Control

Self Cite

131

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show abstract

“…Other methods for testing input-output properties of 2D PDEs without relying on finite-dimensional approximations are generally limited in their application. For example, in [6], [7], LMIs for H ∞ filtering and control of diffusive systems are derived, using a storage function of the form V (u) = u 2 L2 + ∇u, P ∇u L2 , parameterized by a positive matrix P > 0. Similarly, in [8], polynomial constraints N (x, y) ≤ 0 are proposed for testing input-output properties of wallbounded shear flows, also parameterizing a storage function V (u) = 1 2 u, Qu L2 by a positive matrix Q > 0.…”

Section: Introductionmentioning

confidence: 99%

$L_2$-Gain Analysis of Coupled Linear 2D PDEs using Linear PI Inequalities

Declan¹,

Peet²

2022

Preprint

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In this paper, we present a new method for estimating the L 2 -gain of systems governed by 2nd order linear Partial Differential Equations (PDEs) in two spatial variables, using semidefinite programming. It has previously been shown that, for any such PDE, an equivalent Partial Integral Equation (PIE) can be derived. These PIEs are expressed in terms of Partial Integral (PI) operators mapping states in L 2 [Ω], and are free of the boundary and continuity constraints appearing in PDEs. In this paper, we extend the 2D PIE representation to include input and output signals in R n , deriving a bijective map between solutions of the PDE and the PIE, along with the necessary formulae to convert between the two representations. Next, using the algebraic properties of PI operators, we prove that an upper bound on the L 2 -gain of PIEs can be verified by testing feasibility of a Linear PI Inequality (LPI), defined by a positivity constraint on a PI operator mapping R n × L 2 [Ω]. Finally, we use positive matrices to parameterize the cone of positive PI operators on R n × L 2 [Ω], allowing feasibility of the L 2 -gain LPI to be tested using semidefinite programming. We implement this test in the MATLAB toolbox PIETOOLS, and demonstrate that this approach allows an upper bound on the L 2 -gain of PDEs to be estimated with little conservatism.

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“…The results are demonstrated on a model of a 2D catalytic slab (Section 6). Preliminary results on H ∞ filtering under pointlike measurements are presented in [19].…”

Section: Introductionmentioning

confidence: 99%

Delayed H∞ control of 2D diffusion systems under delayed pointlike measurements

Selivanov

Fridman

2019

Automatica

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Up to now, robust control of multi-dimensional diffusion systems was confined to averaged measurements. In this paper, we consider 2D diffusion systems with delayed pointlike measurements. A pointlike measurement is the state value averaged over a small subdomain that approximates its point value. The main novelty enabling the study of such measurements is a new inequality, which we call the reciprocally convex variation of Friedrich's inequality. It bounds the difference between a function and its point values in the L 2-norm using the function's derivatives. Combining this result with a new Lyapunov-Krasovskii functional, which has a spatially-varying kernel, we solve the H∞ control and filtering problems in the presence of time-varying input and output delays. We show that any 2D semilinear diffusion system with pointlike measurements can be stabilized by static output feedback applied through characteristic functions if the controller gain and number of sensors/actuators are large enough while the input and output delays are sufficiently small. The results are demonstrated on a 2D catalytic slab model.

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

Abstract: This is a repository copy of Sampled-data H∞ filtering of a 2D heat equation under pointlike measurements.

Cited by 6 publications

References 20 publications

Survey on time-delay approach to networked control

Survey on time-delay approach to networked control

$L_2$-Gain Analysis of Coupled Linear 2D PDEs using Linear PI Inequalities

Delayed H∞ control of 2D diffusion systems under delayed pointlike measurements

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