Stackelberg法稳定游戏控制系统

IF 1.3 3区数学 Q4 AUTOMATION & CONTROL SYSTEMS

Esaim-Control Optimisation and Calculus of Variations Pub Date : 2023-09-05 DOI:10.1051/cocv/2023060

Yue Sun, Juanjuan Xu, Huanshui Zhang, Renren Zhang

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引用次数: 0

摘要

本文主要研究基于博弈的控制系统的镇定问题。特别是，系统中涉及两个参与者，其中一个是最小化相关的成本函数，另一个是稳定系统。与以往的工作不同，新的贡献是利用Stackelberg博弈方法推导出基于博弈的控制系统镇定的充分必要条件。其关键技术是利用矩阵极大值原理显式求解Stackelberg对策中的正、后向差分方程，并给出最优反馈增益矩阵。

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Stackelberg method to stabilize game-based control system

In this paper, we are concerned with the stabilization problem of the game-based control system. In particular, two players are involved in the system where one is to minimize the related cost function and the other is to stabilize the system. Different from the previous works, the new contribution is to derive the necessary and sufficient condition for the stabilization of the game-based control system by applying Stackelberg game method. The key technique is to explicitly solve the forward and backward difference equations (FBDEs) from the Stackelberg game and give the optimal feedback gain matrix of the leader by using the matrix maximum principle.

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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.