Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



On the ``bang-bang'' control problem

Authors: R. Bellman, I. Glicksberg and O. Gross
Journal: Quart. Appl. Math. 14 (1956), 11-18
MSC: Primary 34.0X
DOI: https://doi.org/10.1090/qam/78516
MathSciNet review: 78516
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Abstract: Let $ S$ be a physical system whose state at any time is described by an $ n$-dimensional vector $ x\left( t \right)$, where $ x\left( t \right)$ is determined by a linear differential equation $ dz/dt = Az$, with $ A$ a constant matrix. Application of external influences will yield an inhomogeneous equation, $ dz/dt = Az + f$, where $ f$, the ``forcing term", represents the control. A problem of some importance in the theory of control circuits is that of choosing $ f$ so as to reduce $ z$ to 0 in minimum time. If $ f$ is restricted to belong to the class of vectors whose $ i$th components can assume only the values $ \pm {b_i}$, the control is said to be of the ``bang-bang'' type.

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

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DOI: https://doi.org/10.1090/qam/78516
Article copyright: © Copyright 1956 American Mathematical Society

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