Gugat M (2019)
Publication Language: English
Publication Type: Journal article, Original article
Publication year: 2019
Book Volume: 4
Pages Range: 849-866
Journal Issue: 4
URI: http://www.ybook.co.jp/online2/oppafa/vol4/p849.html
Open Access Link: http://www.ybook.co.jp/online2/oppafa/vol4/p849.html
In this paper the turnpike phenomenon
is studied for problems of optimal boundary control.
We consider systems that are governed by
a linear $2\times 2$ hyperbolic partial differential equation
with a source term.
Turnpike results are obtained for problems of optimal Dirichlet boundary control
for such systems with
a strongly convex objective function that
depends on the control and the boundary traces of the system states.
In the problem we also allow for a convex inequality constraint.
We show that asymptotically for large $T$ the influence
of the initial state becomes smaller and smaller
in the sense that the $L^2$-norm of the difference
between the dynamic optimal control and the
stationary control that solves the corresponding static optimal control problem
remains uniformly bounded for arbitrarily large $T$.
As an application, we consider gas pipeline flow.
APA:
Gugat, M. (2019). A turnpike result for convex hyperbolic optimal boundary control problems. Pure and Applied Functional Analysis, 4(4), 849-866.
MLA:
Gugat, Martin. "A turnpike result for convex hyperbolic optimal boundary control problems." Pure and Applied Functional Analysis 4.4 (2019): 849-866.
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