Optimal boundary control of 2 × 2 linear hyperbolic PDEs

Hasan, Agus; Imsland, Lars; Ivanov, Ivan Ganchev; Kostova, Snezhana; Bogdanova, Boryana

doi:10.1109/med.2016.7536012

Cited by 4 publications

(1 citation statement)

References 28 publications

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“…In this paper we study optimal Dirichlet boundary control problems for systems that are governed by linear 2 × 2 hyperbolic pdes. A similar problem of optimal boundary control is studied in [20], but the turnpike phenomenon is not considered. Our motivation for this setting is to obtain structural insights for the optimal control of gas flow in pipelines.…”

Section: Introductionmentioning

confidence: 99%

On the Turnpike Phenomenon for Optimal Boundary Control Problems with Hyperbolic Systems

Gugat¹,

Hante²

2019

SIAM J. Control Optim.

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We study problems of optimal boundary control with systems governed by linear hyperbolic partial differential equations. The objective function is quadratic and given by an integral over the finite time interval (0, T ) that depends on the boundary traces of the solution. If the time horizon T is sufficiently large, the solution of the dynamic optimal boundary control problem can be approximated by the solution of a steady state optimization problem. We show that for T → ∞ the approximation error converges to zero in the sense of the norm in L 2 (0, 1) with the rate 1/T , if the time interval (0, T ) is transformed to the fixed interval (0, 1). Moreover, we show that also for optimal boundary control problems with integer constraints for the controls the turnpike phenomenon occurs. In this case the steady state optimization problem also has the integer constraints. If T is sufficiently large, the integer part of each solution of the dynamic optimal boundary control problem with integer constraints is equal to the integer part of a solution of the static problem. A numerical verification is given for a control problem in gas pipeline operations.

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Section: Introductionmentioning

confidence: 99%