On Zhou's maximum principle for near-optimal control of mean-field forward-backward stochastic systems with jumps and its applications

Hafayed, Mokhtar; Abba, Abdelmadjid; Boukaf, Samira

doi:10.1504/ijmic.2016.074292

Cited by 6 publications

(4 citation statements)

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“…Due to Lemma 2, for any κ ∈ [0, (1/3)), by using the similar arguments as developed in [7] the proof of eorem 1, we can also prove that…”

Section: Corollary 1 Under the Assumptions Of Eorem 2 It Holds Thatmentioning

confidence: 67%

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Maximum Principle for Near-Optimality of Mean-Field FBSDEs

2020

Mathematical Problems in Engineering

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The present paper concerns with a near-optimal control problem for systems governed by mean-field forward-backward stochastic differential equations (FBSDEs) with mixed initial-terminal conditions. Utilizing Ekeland’s variational principle as well as the reduction method, the necessary and sufficient near-optimality conditions are established in the form of Pontryagin’s type. The results are obtained under restriction on the convexity of the control domain. As an application, a linear-quadratic stochastic control problem is solved explicitly.

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“…Due to Lemma 2, for any κ ∈ [0, (1/3)), by using the similar arguments as developed in [7] the proof of eorem 1, we can also prove that…”

Section: Corollary 1 Under the Assumptions Of Eorem 2 It Holds Thatmentioning

confidence: 67%

“…Since then, many works have been devoted to the near-optimality of various stochastic control systems. Without being exhaustive, let us refer to [5][6][7][8][9][10][11][12][13] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Maximum Principle for Near-Optimality of Mean-Field FBSDEs

2020

Mathematical Problems in Engineering

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“…Bahlali et al [17] considered a class of nonlinear forward-backward stochastic differential equations and gave the necessary conditions for near optimal control. Hafayed et al [18] concerned with the stochastic maximum principle for near optimal control of nonlinear controlled mean-field forward-backward stochastic systems driven by Brownian motions and random Poisson martingale measure. Wang and Wu [19] and Zhang [20] discussed near optimal problem for the stochastic system with time delay, respectively.…”

Section: Introductionmentioning

confidence: 99%

Near Optimality of Linear Delayed Doubly Stochastic Control Problem

Jun

Lin

2021

Mathematical Problems in Engineering

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In this paper, we study a kind of near optimal control problem which is described by linear quadratic doubly stochastic differential equations with time delay. We consider the near optimality for the linear delayed doubly stochastic system with convex control domain. We discuss the case that all the time delay variables are different. We give the maximum principle of near optimal control for this kind of time delay system. The necessary condition for the control to be near optimal control is deduced by Ekeland’s variational principle and some estimates on the state and the adjoint processes corresponding to the system.

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“…These include the well-known references on system identification (e.g., Soderstrom and Stoica, 1989) and also papers which use statistical probability methods (e.g., Aguero et al, 2012;Behzad et al, 2012;Hafayed et al, 2016. Though their effectiveness in solving both complex theoretical and practical identification cases is not questioned, these techniques are often too complicated for most engineers to apply in practice.…”

Section: Introductionmentioning

confidence: 99%

Extending the Kalman filter for structured identification of linear and nonlinear systems

Best

Bogdanski

2017

IJMIC

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This paper considers a novel approach to system identification which allows accurate models to be created for both linear and nonlinear multi-input/output systems. In addition to conventional system identification applications, the method can also be used as a black-box tool for model order reduction. A nonlinear Kalman filter is extended to include slow-varying parameter states in a canonical model structure. Interestingly, in spite of all model parameters being unknown at the start, the filter is able to evolve parameter estimates to achieve 100% accuracy in noise-free test cases, and is also proven to be robust to noise in the measurements. The canonical structure ensures a well-conditioned model which simultaneously provides valuable dynamic information to the engineer. After extensive testing of a linear example, the model structure is extended to a generalised nonlinear form, which is shown to accurately identify the handling response of a full vehicle model.

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On Zhou's maximum principle for near-optimal control of mean-field forward-backward stochastic systems with jumps and its applications

Cited by 6 publications

References 0 publications

Maximum Principle for Near-Optimality of Mean-Field FBSDEs

Maximum Principle for Near-Optimality of Mean-Field FBSDEs

Near Optimality of Linear Delayed Doubly Stochastic Control Problem

Extending the Kalman filter for structured identification of linear and nonlinear systems

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