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An optimal control model for uncertain systems with time-delay. (English) Zbl 1295.49019

Summary: An uncertain control model with time-delay is investigated based on the concept of uncertain process. The value function of the model is infinite-dimensional in the state. Some conditions are presented to guarantee the model is equivalent to a finite-dimensional one. The latter is solved by the equation of optimality. Then the solution of an uncertain linear quadratic optimal control problem with time-delay is obtained. An example is given to show how to solve an uncertain linear quadratic optimal control model with time-delay. Finally, as an application of the result, an optimal consumption problem with delay in financial market is dealt with.

MSC:

49L20 Dynamic programming in optimal control and differential games
49N10 Linear-quadratic optimal control problems
93A30 Mathematical modelling of systems (MSC2010)
91B42 Consumer behavior, demand theory
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