Optimal Control of Nonlinear Stochastic Differential Equations on Hilbert Spaces

Barbu V, Röckner M, Zhang D (2020)
SIAM Journal on Control and Optimization 58(4): 2383-2410.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Barbu, Viorel; Röckner, MichaelUniBi; Zhang, Deng
Abstract / Bemerkung
We here consider optimal control problems governed by nonlinear stochastic equations on a Hilbert space H with nonconvex payoff, which is rewritten as a deterministic optimal control problem governed by a Kolmogorov equation in H. We prove the existence and first-order necessary condition of closed-loop optimal controls for the above control problem. The strategy is based on solving a deterministic bilinear optimal control problem for the corresponding Kolmogorov equation on the space L-2 (H, nu), where nu is the related infinitesimally invariant measure for the Kolmogorov operator.
Stichworte
stochastic differential equations; optimal control; Kolmogorov operators
Erscheinungsjahr
2020
Zeitschriftentitel
SIAM Journal on Control and Optimization
Band
58
Ausgabe
4
Seite(n)
2383-2410
ISSN
0363-0129
eISSN
1095-7138
Page URI
https://pub.uni-bielefeld.de/record/2946143

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Barbu V, Röckner M, Zhang D. Optimal Control of Nonlinear Stochastic Differential Equations on Hilbert Spaces. SIAM Journal on Control and Optimization. 2020;58(4):2383-2410.
Barbu, V., Röckner, M., & Zhang, D. (2020). Optimal Control of Nonlinear Stochastic Differential Equations on Hilbert Spaces. SIAM Journal on Control and Optimization, 58(4), 2383-2410. doi:10.1137/19M1307615
Barbu, V., Röckner, M., and Zhang, D. (2020). Optimal Control of Nonlinear Stochastic Differential Equations on Hilbert Spaces. SIAM Journal on Control and Optimization 58, 2383-2410.
Barbu, V., Röckner, M., & Zhang, D., 2020. Optimal Control of Nonlinear Stochastic Differential Equations on Hilbert Spaces. SIAM Journal on Control and Optimization, 58(4), p 2383-2410.
V. Barbu, M. Röckner, and D. Zhang, “Optimal Control of Nonlinear Stochastic Differential Equations on Hilbert Spaces”, SIAM Journal on Control and Optimization, vol. 58, 2020, pp. 2383-2410.
Barbu, V., Röckner, M., Zhang, D.: Optimal Control of Nonlinear Stochastic Differential Equations on Hilbert Spaces. SIAM Journal on Control and Optimization. 58, 2383-2410 (2020).
Barbu, Viorel, Röckner, Michael, and Zhang, Deng. “Optimal Control of Nonlinear Stochastic Differential Equations on Hilbert Spaces”. SIAM Journal on Control and Optimization 58.4 (2020): 2383-2410.

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