一般不定倒向随机线性二次最优控制问题

IF 1.3 3区数学 Q4 AUTOMATION & CONTROL SYSTEMS Esaim-Control Optimisation and Calculus of Variations Pub Date : 2022-02-28 DOI:10.1051/cocv/2022030

Jingrui Sun, Jiaqiang Wen, J. Xiong

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引用次数: 2

摘要

研究一类一般的后向随机线性二次最优控制问题，该问题的状态方程和代价泛函都包含非齐次项。该问题的主要特点是允许代价函数中的权重矩阵是不定的，并且在控制和状态过程中存在交叉积项。得到了问题可解的充分必要条件，并给出了最优控制的正反向随机微分方程的表征。利用Riccati方程方法，给出了构造最优控制的一般方法，并明确地得到了最优控制的值函数。

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General indefinite backward stochastic linear-quadratic optimal control problems

A general backward stochastic linear-quadratic optimal control problem is studied, in which both the state equation and cost functional contain the nonhomogeneous terms. The main feature of the problem is that the weighting matrices in the cost functional are allowed to be indefinite and cross-product terms in the control and the state processes are present. Necessary and sufficient conditions for the solvability of the problem are obtained, and a characterization of the optimal control in terms of forward-backward stochastic differential equations is derived. By a Riccati equation approach, a general procedure for constructing optimal controls is developed and the value function is obtained explicitly.

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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.