A General Maximum Principle for Progressive Optimal Stochastic Control Problems with Markov Regime-Switching

IF 1.3 3区数学 Q4 AUTOMATION & CONTROL SYSTEMS

Esaim-Control Optimisation and Calculus of Variations Pub Date : 2022-08-25 DOI:10.1051/cocv/2022054

Yuanzhuo Song, Zhanghua Wu

引用次数: 2

Abstract

In this paper, we give a general maximum principle for optimal controls of stochastic systems driven by Markov chains. The control is allowed to enter both diffusion and jump terms and the control domain is not necessarily convex. We apply a new spike variation and the stochastic integral of progressive processes to obtain the main result.

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马尔可夫状态切换渐进最优随机控制问题的一般极大值原理

本文给出了马尔可夫链驱动的随机系统最优控制的一般极大值原理。控制允许同时进入扩散项和跳跃项，并且控制域不一定是凸的。我们应用了一个新的尖峰变化和渐进过程的随机积分来得到主要结果。

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

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.

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