具有马尔可夫链的部分可观测平均场随机系统渐进最优控制的一般极大值原理。

IF 1.3 3区数学 Q4 AUTOMATION & CONTROL SYSTEMS

Esaim-Control Optimisation and Calculus of Variations Pub Date : 2023-07-10 DOI:10.1051/cocv/2023050

Tian Chen, Y. Jia

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引用次数: 0

摘要

研究了一类具有马尔可夫链的部分观测型平均场随机控制系统的最优控制问题。允许控制变量进入状态过程的扩散项和观测过程的漂移项。控制域不必是凸的。在我们的模型中，代价函数和观测值也是平均场型的。利用特殊的尖峰变化，得到了相关的随机极大值原理。渐进结构的随机极大值原理与经典情况有本质的区别。

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A general maximum principle for progressive optimal control of partially observed mean-field stochastic system with markov chain.

In this paper, we study an optimal control problem of partially observed mean-field type stochastic control system with Markov chain in progressive structure. The control variable is allowed to enter the diffusion term of the state process and the drift term of the observation process. The control domain need not be convex. In our model, the cost functional and the observation are also of mean-field type. By virtue of a special spike variation, the related stochastic maximum principle has been obtained. The stochastic maximum principle in progressive structure is essentially different from the classical case.

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来源期刊

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

自引率

7.10%

发文量

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.