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An example of a perturbation-type extremum controller

Published online by Cambridge University Press:  14 July 2016

D. M. Titterington*
Affiliation:
University of Glasgow

Abstract

Controls of the perturbation type are evolved for the purpose of monitoring the random movement of a response curve using noise-corrupted observations of the response. Dynamic programming methods are used to obtain approximations to the optimum control system when the response is quadratic. Further results are briefly described.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 1974 

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References

Anderson, W. J. (1969) Local behaviour of solutions of stochastic integral equations. . McGill University, Montreal.Google Scholar
Bather, J. A. (1968) A diffusion model for the control of a dam. J. Appl. Prob. 5, 5571.Google Scholar
Box, G. E. P. and Chanmugam, J. (1962) Adaptive optimization of continuous processes. I and EC Fundamentals 1, 216.CrossRefGoogle Scholar
Box, G. E. P. and Draper, N. R. (1969) Evolutionary Operation. Wiley, New York.Google Scholar
Bucy, R. S. and Joseph, P. D. (1968) Filtering for Stochastic Processes with Applications to Guidance. Interscience Tracts in Mathematics. Wiley, New York.Google Scholar
Frost, P. A. and Kailath, T. (1971) An innovations approach to least-squares estimation — part III: nonlinear estimation in white Gaussian noise. IEEE Trans. Aut. Control AC-16, 217226.Google Scholar
Jazwinski, A. H. (1970) Stochastic Processes and Filtering Theory. Academic Press, New York.Google Scholar
Mckean, H. P. (1969) Stochastic Integrals. Academic Press, New York.Google Scholar
Mandl, P. (1968) Analytical Treatment of One-Dimensional Markov Processes. Springer-Verlag, Berlin.Google Scholar
Morton, R. (1971) On the optimal control of stationary diffusion processes with inaccessible boundaries and no discounting. J. Appl. Prob. 8, 551560.Google Scholar
Roberts, J. D. (1965) Extremum or hill-climbing regulation: a statistical theory involving lags, disturbances and noise. Proc. IEE 112, 137150.Google Scholar
Titterington, D. M. (1971) The adaptive optimisation of yield. . University of Cambridge.Google Scholar
Titterington, D. M. (1973) A method of extremum adaptation. J. Inst. Math. Applics. 11, 297315.Google Scholar