非圆柱域中退化方程耦合系统的纳什-斯塔克尔伯格可控性

Stackelberg-Nash可控性 for 一个多目标Stefan问题

Stackelberg-Nash controllability for a multi-objective Stefan problem

本文研究了一维Stefan系统在局部分布式控制下的分层控制问题，结合Stackelberg策略与多个追随者的Nash均衡，形成多目标自由边界问题。通过分析分层控制与移动界面的相互作用，证明原问题可转化为该最优系统null可控性问题，并在合适几何条件下建立局部null可控性结果。

Stackelberg exact controllability of a class of nonlocal parabolic equations

This paper deals with a multi-objective control problem for a class of nonlocal parabolic equations, where the non-locality is expressed through an integral kernel. We present the Stackelberg strategy that combines the concepts of controllability to trajectories with optimal control. The strategy involves two controls: a main control (the leader) and a secondary control (the follower). The leader solves a controllability to trajectories problem which consists to drive the state of the system to a prescribed target at a final time while the follower solves an optimal control problem which consi…

Hierarchic Controllability for a nonlinear parabolic equation in one dimension

This paper deals with the hierarchical control of the parabolic equation.We use Stackelberg{Nash strategies. As usual, we consider one leader and two followers. To each leader we associate a Nash equilibrium corresponding to a bi-objective optimal control problem, then, we look for a leader that solves null controllability e with trajectories problem. We consider linear and nonlinear equations in dimension 1.

非柱状区域上线性波动方程多目标可控性问题的理论分析

Theoretical analysis of a multi-objective controllability problem for the linear wave equation on a non-cylindrical domain

本文基于Stackelberg策略研究移动域内一维线性波动方程的分层可控性问题，通过在部分边界施加领导者与跟随者控制建立均衡策略。

关于运动区域中线性化微极流体系统分层控制的注记

Remarks on Hierarchic Control for a Linearized Micropolar Fluids System in Moving Domains

本文研究运动边界区域内线性化微极流体方程的分层Stackelberg控制策略，推导纳什均衡的存在唯一性与刻画、系统对领导者控制的近似能控性，以及Stackelberg-Nash问题的适定性与领导者最优性系统。

非柱状域中一维波动方程的能控性

Controllability for a One-Dimensional Wave Equation in a Non-cylindrical Domain

本文研究非柱状域中混合边界条件下一维波动方程的能控性，通过引入主从控制并采用Stackelberg-Nash策略解决该问题。

Controllability of quasi-linear Hamiltonian NLS equations

We prove internal controllability in arbitrary time, for small data, for quasi-linear Hamiltonian NLS equations on the circle. We use a procedure of reduction to constant coefficients up to order zero and HUM method to prove the controllability of the linearized problem. Then we apply a Nash-Moser-Hörmander implicit function theorem as a black box.

具有Hardy势的抛物方程的分层精确可控性

Hierarchical exact controllability for a parabolic equation with Hardy potential

本文通过Stackelberg-Nash策略研究具有Hardy势的抛物方程的分层精确可控性，在线性和半线性情形下分别利用Carleman不等式和不动点定理证明了领导者的存在性。

非退化拟线性抛物系统的分层局部零能控性

Hierarchical local null controllability for a non-degenerate quasi-linear parabolic system

该论文针对有界区间上的非退化拟线性抛物系统，采用含领导者与追随者控制的Stackelberg-Nash策略，先证明线性系统的Carleman不等式，再通过Liusternik反函数定理得到拟线性系统的局部零能控性。

具有非局部系数的退化抛物方程的分层零能控性

Hierarchical null controllability of a degenerate parabolic equation with nonlocal coefficient

本文针对扩散系数为空间退化函数与非局部项乘积的抛物方程，采用Stackelberg-Nash策略结合卡尔曼估计与Liusternik逆函数定理，证明其局部零能控性，解决了非局部系数导致的乘法耦合计算问题。

Exact controllability for quasi-linear perturbations of KdV

We prove that the KdV equation on the circle remains exactly controllable in arbitrary time with localized control, for sufficiently small data, also in presence of quasi-linear perturbations, namely nonlinearities containing up to three space derivatives, having a Hamiltonian structure at the highest orders. We use a procedure of reduction to constant coefficients up to order zero, classical Ingham inequality and HUM method to prove the controllability of the linearized operator. Then we prove and apply a modified version of the Nash-Moser implicit function theorems by Hörmander.

带固定端点控制的一维波动方程的近似能控性

Approximate controllability for a one-dimensional wave equation with the fixed endpoint control

本文研究带移动边界的一维波动方程的近似能控性，在移动端点速度小于特征速度的条件下，确立了方程能控性，给出了纳什均衡存在唯一性、领导者控制近似能控性及最优性系统等结果。

具有双线性控制的一维线性和非线性薛定谔方程的局部能控性

Local controllability of 1D linear and nonlinear Schrödinger equations with bilinear control

我们考虑一个线性薛定谔方程，在一个有界的区间上，双线性控制，它代表了一个量子粒子在一个电场（控制）。我们证明了这个系统的可控性，在任何积极的时间，当地的基态。对于特定的模型，也证明了类似的结果（第一作者和J.M. Coron），证明依赖于Nash-Moser隐函数定理，以处理正则性的先验损失。本文的模型更一般，空间是最优的，对时间没有限制，证明依赖于经典的逆映射定理。一个隐藏的正则化效应被强调，表明实际上没有损失的规律性。然后，同样的策略被应用到非线性薛定谔方程和非线性波动方程，表明该方法适用于广泛的双线性控制系统。

纪念Luiz Adauto Medeiros教授：Oldroyd方程的层级控制

Hierarchical Control for the Oldroyd Equation in Memoriam to Professor Luiz Adauto Medeiros

本文针对带非正则系数的Oldroyd方程，研究Stackelberg-Nash策略下的层级控制问题，证明了Nash均衡的存在唯一性，得到领导者控制的近似可控性及最优性系统。

带动态边界条件的随机抛物方程多目标控制

Multi-objective control for stochastic parabolic equations with dynamic boundary conditions

本文针对带动态边界条件的随机抛物方程，提出分层多目标控制框架，通过Nash和Stackelberg策略结合Carleman估计与控制对偶方法，实现领导者的零可控性与跟随者的状态跟踪目标。

关于非柱形区域中波动方程的分层控制的注记

Remarks on hierarchic control for the wave equation in a non cylindrical domain

本文在非柱形区域中建立波动方程的分层控制，基于Stackelberg博弈将控制分为领导者和跟随者，证明了存在唯一性并给出最优性系统。