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Adaptive control for semilinear stochastic systems
Duncan, Tyrone E. Maslowski, Bozenna J. Pasik-Duncan, Bozenna
Duncan, Tyrone E.
Maslowski, Bozenna J.
Pasik-Duncan, Bozenna
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Abstract
An adaptive, ergodic cost stochastic control problem for a partially known, semilinear, stochastic system in an infinite dimensional space is formulated and solved. The solutions of the Hamilton--Jacobi--Bellman equations for the discounted cost and the ergodic cost stochastic control problems require some special interpretations because they do not typically exist in the usual sense. The solutions of the parameter dependent ergodic Hamilton--Jacobi--Bellman equations are obtained from some corresponding discounted cost control problems as the discount rate tends to zero. The solutions of the ergodic Hamilton--Jacobi--Bellman equations are shown to depend continuously on the parameter. A certainty equivalence adaptive control is given that is based on the optimal controls from the solutions of the ergodic Hamilton--Jacobi--Bellman equations and a strongly consistent family of estimates of the unknown parameter. This adaptive control is shown to achieve the optimal ergodic cost for the known system.
Description
This is the published version, also available here: http://www.dx.doi.org/10.1137/S0363012999351826.
Date
2000-01-01
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Society for Industrial and Applied Mathematics
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Keywords
stochastic adaptive control, ergodic control, stochastic semilinear systems, stochastic optimal control, distributed parameter systems
Citation
Duncan, Tyrone E. "Adaptive control for semilinear stochastic systems." SIAM J. Control Optim. (2000) 38, 6. 1683-1706. http://www.dx.doi.org/10.1137/S0363012999351826.