Differential Inclusions, Control and Optimization 21 (2001) 97-126
doi: 10.7151/dmdico.1019

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OPTIMAL CONTROL OF ∞-DIMENSIONAL STOCHASTIC SYSTEMS VIA GENERALIZED SOLUTIONS OF HJB EQUATIONS

N.U. Ahmed

Department of Mathematics
University of Ottawa
Ottawa, Canada, K1N6N5

Abstract

In this paper, we consider optimal feedback control for stochastc infinite dimensional systems. We present some new results on the solution of associated HJB equations in infinite dimensional Hilbert spaces. In the process, we have also developed some new mathematical tools involving distributions on Hilbert spaces which may have many other interesting applications in other fields. We conclude with an application to optimal stationary feedback control.

Keywords: optimal control, stochastic systems, infinite dimension, HJB equation, stationary feedback control.

2000 Mathematics Subject Classification: 93E20, 49J27, 49K45.

References

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Received 30 June 2000