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Dynamic programming, pattern recognition and location of faults in complex systems

Published online by Cambridge University Press:  14 July 2016

Richard Bellman*
Affiliation:
The RAND Corporation, Santa Monica, California

Abstract

In a previous paper devoted to an application of dynamic programming to pattern recognition [1], we pointed out that some identification problems could be regarded as generalized trajectory processes. The functional equation technique [2] could then be employed to obtain an analytic formulation of the determination of optimal search techniques. In many cases, however, (for example, in chess or checkers), a straightforward use of the functional equation is impossible because of dimensionality difficulties. In circumventing these obstacles to effective computational solution, we employed a decomposition technique which we called “stratification” [1, 3]. In this paper, we present a different way of avoiding the dimensionality problem, based upon the concept of “extended state variable”. To indicate the utility of the concept, we shall apply it to the problem of finding a fault in a complex system.

Type
Short Communications
Copyright
Copyright © Sheffield: Applied Probability Trust 

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References

[1] Bellman, R. (1964) System identification, pattern recognition, and dynamic programming. Hughes Research Laboratories Research Report No. 327.Google Scholar
[2] Bellman, R. (1963) Adaptive Control Processes: A Guided Tour. Princeton University Press, Princeton.Google Scholar
[3] Bellman, R. (1965) An application of dynamic programming to the determination of optimal play in chess and checkers. Proc. Nat. Acad. Sci. 53, 244246.CrossRefGoogle Scholar
[4] Bellman, R. and Dreyfus, S. (1962) Applied Dynamic Programming, Princeton University Press, Princeton.CrossRefGoogle ScholarPubMed
[5] Ford, L. R. Jr. and Fulkerson, D. R. (1962) Flows in Networks, Princeton University Press, Princeton.Google Scholar