Asymptotic analysis and error estimates for an optimal control problem with oscillating boundaries

Nandakumaran, A. K.; Prakash, Ravi; Raymond, JP

doi:10.1007/s11565-011-0135-3

Cited by 19 publications

(9 citation statements)

References 22 publications

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“…The domain is a standard one considered by many authors in the literature. See, for example , and so on. The domain Ω ε consists of bottom and upper parts, respectively, denoted by Ω − and

{normalΩ}_{ε}^{+}

(Figure ).…”

Section: Introductionmentioning

confidence: 99%

“…In and , the authors have studied controls problems with control acting away from the oscillating part of the domain. In this paper, we consider controls on the boundary of the oscillating part through Neumann condition which seems to be more complicated.…”

Section: Introductionmentioning

confidence: 99%

“…There is also a large amount of literature on the homogenization with oscillating boundaries, which has tremendous applications as well (for example, , , and ). For some recent work on oscillating boundaries, see and .…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Asymptotic analysis of Neumann periodic optimal boundary control problem

Nandakumaran

Prakash

Sardar

2016

Math Methods in App Sciences

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An optimal boundary control problem in a domain with oscillating boundary has been investigated in this paper. The controls are acting periodically on the oscillating boundary. The controls are applied with suitable scaling parameters. One of the major contribution is the representation of the optimal control using the unfolding operator. We then study the limiting analysis (homogenization) and obtain two limit problems according to the scaling parameters. Another notable observation is that the limit optimal control problem has three controls, namely, a distributed control, a boundary control, and an interface control.

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“…The domain is a standard one considered by many authors in the literature. See, for example , and so on. The domain Ω ε consists of bottom and upper parts, respectively, denoted by Ω − and

{normalΩ}_{ε}^{+}

(Figure ).…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Asymptotic analysis of Neumann periodic optimal boundary control problem

Nandakumaran

Prakash

Sardar

2016

Math Methods in App Sciences

Self Cite

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“…The spatial scales are not present in the model, because it is assumed that all heat is released into the fluid at a point [27]. Inclusion of spatial and temporal scales is considered in various homogenization problems, which encompasses the asymptotic analysis of solutions of PDEs of periodic structures [4], [16], [25]. Asymptotic expansion is used to derive the homogenized equation, however the method is formal and the second step is needed to prove the convergence as the ratio of the size of the period to the size of a sample of the medium goes to zero [1].…”

Section: Introductionmentioning

confidence: 99%

Self-excited Oscillations and Fuel Control of a Combustion Process in a Rijke Tube

Pušenjak

Ticar

Oblak

2014

International Journal of Nonlinear Sciences and Numerical Simulation

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This paper treats the control of nonstationary oscillations of the pressure which arise in the combustion process of a Rijke tube. The low order model of a nonstationary combustion process in a Rijke tube with mul tiplicative feedback control function is considered, which is investigated by means of two-DOF coupled van der Pol oscillator. The self-excited oscillations in the combustion process are analysed by means of the Extended Lindstedt-Poincare (EL-P) method with multiple time scales. By applying the EL-P method, it is ascertained, that nonstationary oscillations are almost periodic with amplitude and phase, which are functions of the slow time scale. Without control of the fuel influx, the self excited oscillations can approach limit cycles. By applying the fuel control, the influence of control parameters on the quenching of the self excited oscillations is investigated in a phenomenon of competitive quenching and mutual synchronization with close frequencies and multiple harmonics, respectively.

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“…Optimal control problems in domains with highly oscillating boundary are considered in [16,17,19,20,35]. Exact controllability in perforated domains is studied in [12,13].…”

Section: Introductionmentioning

confidence: 99%

Exact internal controllability for a hyperbolic problem in a domain with highly oscillating boundary

Maio

Nandakumaran

2013

Asymptotic Analysis

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In this paper, by using the Hilbert Uniqueness Method (HUM), we study the exact controllability problem described by the wave equation in a three-dimensional horizontal domain bounded at the bottom by a smooth wall and at the top by a rough wall. The latter is assumed to consist in a plane wall covered with periodically distributed asperities whose size depends on a small parameter ε > 0, and with a fixed height. Our aim is to obtain the exact controllability for the homogenized equation.In the process, we study the asymptotic analysis of wave equation in two setups, namely solution by standard weak formulation and solution by transposition method.

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Asymptotic analysis and error estimates for an optimal control problem with oscillating boundaries

Cited by 19 publications

References 22 publications

Asymptotic analysis of Neumann periodic optimal boundary control problem

Asymptotic analysis of Neumann periodic optimal boundary control problem

Self-excited Oscillations and Fuel Control of a Combustion Process in a Rijke Tube

Exact internal controllability for a hyperbolic problem in a domain with highly oscillating boundary

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