Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Notes on matrix theory. X. A problem in control

Author: Richard Bellman
Journal: Quart. Appl. Math. 14 (1957), 417-419
MSC: Primary 34.0X
DOI: https://doi.org/10.1090/qam/82592
MathSciNet review: 82592
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Abstract: In the theory of control processes, it is important to be able to calculate $ \smallint _0^\infty \left( {x,Bx} \right)dt$ without having to solve explicitly the differential equation $ dx/dt = Ax, \\ x\left( 0 \right) = c$. A method for doing this is presented in this paper, generalizing one due to Anke for $ n$th order linear differential equations.

References [Enhancements On Off] (What's this?)

  • [1] Klaus Anke, Eine neue Berechnungsmethode der quadratischen Regelfläche, Z. ang. Math. u. Phys. 6 327-331 (1955) MR 0074600
  • [2] H. Bückner, A formula for an integral occurring in the theory of linear servomechanisms and control systems, Quart. Appl. Math. 10 (1952) MR 0049253
  • [3] P. Hazenbroek and B. I. Van der Waerden, Theoretical considerations in the optimum adjustment of regulators, Trans. Am. Soc. Mech. Engrs. 72 (1950) MR 0034934

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DOI: https://doi.org/10.1090/qam/82592
Article copyright: © Copyright 1957 American Mathematical Society

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