Stochastic Maximum Principle for Optimal Control of SPDEs

Fuhrman, Marco; Hu, Ying; Tessitore, Gianmario

doi:10.1007/s00245-013-9203-7

Cited by 93 publications

(74 citation statements)

References 15 publications

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“…Nevertheless, it is used with respect to X (·, ·) in (3.33), but not the X (·). This is totally different from the case of SDEs or stochastic evolution equations ( [6,8,10,13]). As a tradeoff, it is too special to cover the result in e.g., Section 3.4.1 next.…”

Section: Maximum Principles Of Optimal Control Problems For Sviesmentioning

confidence: 87%

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Necessary conditions of Pontraygin’s type for general controlled stochastic Volterra integral equations

Wang

2020

ESAIM: COCV

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This article is addressed to giving a solution to a unsolved problem, i.e., to establish the necessary optimality conditions of Pontraygin’s type for controlled stochastic Volterra integral equations (SVIEs) when the control region is non-convex and the control variable enters into the diffusion. This problem has been open since [J. Yong, Stochastic Process Appl. 116 (2006) 779–795] obtained the analogue result for the case of convex control region. The key is to introduce a pair of suitable second-order adjoint processes (SOAPs). It is found that the usual way of using only one SOAP in the maximum condition for the classical setting of controlled stochastic differential equations does not work here.

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Section: Maximum Principles Of Optimal Control Problems For Sviesmentioning

confidence: 87%

“…Remark 3.16. As to the maximum principle of SVIEs, we choose to use SOAP, the idea of which is similar to that in [6,8,10].…”

Section: Maximum Principles Of Optimal Control Problems For Sviesmentioning

confidence: 99%

Necessary conditions of Pontraygin’s type for general controlled stochastic Volterra integral equations

Wang

2020

ESAIM: COCV

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“…Now we will return to estimates to obtain the maximum principle. where P is the solution to the equation (7). Then, lim ǫ→0 sup t∈T E( ∆ ǫ (t) 2 ) = 0 (37)…”

Section: A Stochastic Maximum Principlementioning

confidence: 99%

Existence of optimal controls for SPDE with locally monotone coefficients

Coayla‐Teran

Magalhães

Ferreira

2018

International Journal of Control

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“…Their approach and result looked restrictive due to some technical assumptions. In [5] as well as its long version [6], the authors considered a concrete stochastic parabolic PDE with deterministic coefficients. The approach there, including a compactness argument, required the Markov structure of the system.…”

Section: 1) Dx(t) = [A(t)x(t) + F (T X(t) U(t))]dt + [B(t)x(t) + mentioning

confidence: 99%

A Maximum Principle for Optimal Control of Stochastic Evolution Equations

Meng²

2013

SIAM J. Control Optim.

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A general maximum principle is proved for optimal controls of abstract semilinear stochastic evolution equations. The control variable and linear unbounded operators act in both drift and diffusion terms, and the control set need not be convex. Abstract. A general maximum principle is proved for optimal controls of abstract semilinear stochastic evolution equations. The control variable, as well as linear unbounded operators, acts in both drift and diffusion terms, and the control set need not be convex.

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Stochastic Maximum Principle for Optimal Control of SPDEs

Abstract: Abstract.In this note, we give the stochastic maximum principle for optimal control of stochastic PDEs in the general case (when the control domain need not be convex and the diffusion coefficient can contain a control variable).

Cited by 93 publications

References 15 publications

Necessary conditions of Pontraygin’s type for general controlled stochastic Volterra integral equations

Necessary conditions of Pontraygin’s type for general controlled stochastic Volterra integral equations

Existence of optimal controls for SPDE with locally monotone coefficients

A Maximum Principle for Optimal Control of Stochastic Evolution Equations

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