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.
- Klaus Anke, Eine neue Berechnungsmethode der quadratischen Regelfläche, Z. Angew. Math. Phys. 6 (1955), 327–331 (German). MR 74600, DOI https://doi.org/10.1007/BF01587631
- Hans Bückner, A formula for an integral occurring in the theory of linear servomechanisms and control-systems, Quart. Appl. Math. 10 (1952), 205–213. MR 49253, DOI https://doi.org/10.1090/S0033-569X-1952-49253-1
- P. Hazebroek and B. L. van der Waerden, The optimum adjustment of regulators, Trans. A.S.M.E. 72 (1950), 317–322. MR 34934
Klaus Anke, Eine neue Berechnungsmethode der quadratischen Regelfläche, Z. ang. Math. u. Phys. 6 327-331 (1955)
H. Bückner, A formula for an integral occurring in the theory of linear servomechanisms and control systems, Quart. Appl. Math. 10 (1952)
P. Hazenbroek and B. I. Van der Waerden, Theoretical considerations in the optimum adjustment of regulators, Trans. Am. Soc. Mech. Engrs. 72 (1950)
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Article copyright:
© Copyright 1957
American Mathematical Society