An existence theorem for optimal control systems with state variable inC, and stochastic control problems

  • Richard F. Baum
Contributed Papers


We consider an existence theorem for control systems whose state variables for everyt are inC, the set of continuous functions varying over a given setI. The dependence of the state variables upona ε I is induced by their dependence upon the initial state and the state equation governing the system. In contrast, the controlu=u(t) is taken as a measurable function oft alone. The usual space constraints and boundary conditions are also allowed to vary overaεI, and the cost functional is now taken to be a continuous functional over a suitable class of continuous functions. We also discuss an application of these results to control systems with stochastic boundary conditions.


Boundary Condition Control System Continuous Function Control Problem Measurable Function 
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    Cesari, L.,Existence Theorems for Weak and Usual Optimal Solutions in Lagrange Problems with Unilateral Constraints, I, Transactions of the American Mathematical Society, Vol. 124, No. 3, 1966.Google Scholar
  3. 3.
    Baum, R.,Optimal Control Systems with Stochastic Boundary Conditions, University of Michigan, Ph.D. Thesis, 1969.Google Scholar

Additional Bibliography

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    Fleming, W. H.,Optimal Continuous-Parameter Stochastic Control, SIAM Review, Vol. 11, No. 4, 1969.Google Scholar
  2. 5.
    Kushner, H. J.,On the Existence of Optimal Stochastic Controls, SIAM Journal on Control, Vol. 3, No. 3, 1965.Google Scholar

Copyright information

© Plenum Publishing Corporation 1970

Authors and Affiliations

  • Richard F. Baum
    • 1
  1. 1.Department of Industrial EngineeringUniversity of MichiganAnn Arbor

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