Nonlinear optimal stochastic control — some approximations when the noise is small

  • J. D. Perkins
  • R. W. H. Sargent
Optimal Control Stochastic
Part of the Lecture Notes in Computer Science book series (LNCS, volume 41)


Stochastic control problems for a rather general class of nonlinear systems have been considered in this paper. Deterministic models for the prediction of expected performance have been presented, and it has been shown that optimal controllers designed using the models are good approximations to the true optimal controllers for the stochastic system. Some results have been presented on the use of an estimator coupled with an optimal controller based on continuous observation of the state.

The problems associated with the non-Markov nature of the system, and relaxation of the smoothness conditions imposed on the state and control laws will be the subject of a separate paper.


Performance Index Optimal Controller Nonlinear Stochastic System Stochastic Control Problem Optimal Control Policy 


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    Perkins, J. D., "Optimal Stochastic Control of Continuous Processes — Some Approximations Applicable to Chemical Engineering Problems", Ph.D. Thesis, London (1976)Google Scholar
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    Wonham, W. M., "On the Separation Theorem of Stochastic Control", SIAM J. Control, 6 (2), 312 (1968)Google Scholar
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    Jazwinski, A. H., "Stochastic Processes and Filtering Theory", (Academic Press, New York, 1970)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1976

Authors and Affiliations

  • J. D. Perkins
    • 1
  • R. W. H. Sargent
    • 2
  1. 1.Department of Chemical EngineeringUniversity of CambridgeUK
  2. 2.Department of Chemical Engineering and Chemical TechnologyImperial CollegeLondon

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