A mean-field stochastic linear-quadratic optimal control problem with jumps under partial information

IF 1.3 3区数学 Q4 AUTOMATION & CONTROL SYSTEMS

Esaim-Control Optimisation and Calculus of Variations Pub Date : 2022-05-05 DOI:10.1051/cocv/2022039

Yiyun Yang, M. Tang, Qingxin Meng

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引用次数: 2

Abstract

In this article, the stochastic linear-quadratic optimal control problem of mean-field type with jumps under partial information is discussed. The state equation contains affine terms is a SDE with jumps driven by a multidimensional Brownian motion and a Poisson random martingale measure, the cost function containing cross terms is quadratic, in addition, the state and the control as well as their expectations are contained both in the state equation and the cost functional. Firstly, we prove the existence and uniqueness of the optimal control, and by using Pontryagin’s maximum principle we get the dual characterization of optimal control; Secondly, by introducing the adjoint processes of the state equation, establishing a stochastic Hamiltonian system and using decoupling technology, we deduce two integro-differential Riccati equations and get the feedback representation of the optimal control under partial information; Thirdly, the existence and uniqueness of the solutions of the two associated integro-differential Riccati equations are proved; Finally, we discuss a special case, and by means of filtering technique, establish the corresponding the filtering state feedback representation of the optimal control.

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部分信息下具有跳变的平均场随机线性二次最优控制问题

讨论了在部分信息条件下具有跳变的平均场型随机线性二次最优控制问题。包含仿射项的状态方程是一个由多维布朗运动和泊松随机鞅测度驱动的跳跃的SDE，包含交叉项的代价函数是二次的，并且状态和控制及其期望都包含在状态方程和代价泛函中。首先证明了最优控制的存在唯一性，并利用庞特里亚金极大值原理得到了最优控制的对偶性质;其次，通过引入状态方程的伴随过程，建立随机哈密顿系统，利用解耦技术推导出两个积分-微分Riccati方程，得到了部分信息下最优控制的反馈表示;第三，证明了这两个相关的积分-微分Riccati方程解的存在唯一性;最后，讨论了一种特殊情况，并利用滤波技术，建立了相应的最优控制的滤波状态反馈表示。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Esaim-Control Optimisation and Calculus of Variations Mathematics-Computational Mathematics

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7.10%

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期刊介绍： ESAIM: COCV strives to publish rapidly and efficiently papers and surveys in the areas of Control, Optimisation and Calculus of Variations. Articles may be theoretical, computational, or both, and they will cover contemporary subjects with impact in forefront technology, biosciences, materials science, computer vision, continuum physics, decision sciences and other allied disciplines. Targeted topics include: in control: modeling, controllability, optimal control, stabilization, control design, hybrid control, robustness analysis, numerical and computational methods for control, stochastic or deterministic, continuous or discrete control systems, finite-dimensional or infinite-dimensional control systems, geometric control, quantum control, game theory; in optimisation: mathematical programming, large scale systems, stochastic optimisation, combinatorial optimisation, shape optimisation, convex or nonsmooth optimisation, inverse problems, interior point methods, duality methods, numerical methods, convergence and complexity, global optimisation, optimisation and dynamical systems, optimal transport, machine learning, image or signal analysis; in calculus of variations: variational methods for differential equations and Hamiltonian systems, variational inequalities; semicontinuity and convergence, existence and regularity of minimizers and critical points of functionals, relaxation; geometric problems and the use and development of geometric measure theory tools; problems involving randomness; viscosity solutions; numerical methods; homogenization, multiscale and singular perturbation problems.