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- Title
Optimal boundary control of string vibrations by a force under elastic fixing.
- Authors
Nikitin, A.
- Abstract
We study a boundary control problem based on a mixed problem with an inhomogeneous condition of the second kind at the left end of a string with elastically fixed right end. The difficulty in the solution of that problem is that the fixing condition is absent. Therefore, in addition to a constraint that is an equality of functions in the class L, we need one more condition, to which V.A. Il'in refers as a condition of coordination of the initial and terminal displacements. We develop a new optimization method based on the extension of the terminal conditions to the interval [− T,T]. This permits one to minimize the integral of the squared boundary control. A control minimizing this energy integral is written out in closed form.
- Subjects
BOUNDARY value problems; MATHEMATICAL optimization; INTEGRAL equations; DIFFERENTIAL equations; INTERVAL functions
- Publication
Differential Equations, 2011, Vol 47, Issue 12, p1796
- ISSN
0012-2661
- Publication type
Article
- DOI
10.1134/S0012266111120081