arXiv 2209.044412022-09-08math.OC

Stackelberg strategy on a degenerate parabolic equation with missing data

Landry Djomegne, Cyrille Kenne, Romario Gildas Foko Tiomela

英文摘要：

This paper deals with the hierarchic control of a degenerate parabolic equation with missing initial condition. We present a Stackelberg strategy combining the concept of null controllability with low-regret control. We assume that we can act on the system through a set of hierarchic controls. The main control called the leader is in charge of the null controllability while the second control named the follower solves an optimal control problem involving a missing data. The main novelty of this work is the derivation of a new Carleman inequality for a degenerate system, which is used in a standard way to show observability inequality of the adjoint degenerate systems.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

可测集的能观性不等式与退化抛物方程的Stackelberg-Nash博弈问题

Observability Inequality from Measurable Sets and the Stackelberg-Nash Game Problem for Degenerate Parabolic Equations

本研究借助Carleman估计等工具建立退化抛物方程的可测集能观性不等式，应用于Stackelberg-Nash博弈均衡存在性证明，并分析均衡集与范数最优控制问题。

2023-06-14math.OC

Robust Stackelberg controllability for a parabolic equation

The aim of this paper is to perform a Stackelberg strategy to control parabolic equations. We have one control, \textit{the leader}, that is responsible for a null controllability property; additionally, we have a control \textit{the follower} that solves a robust control objective. That means, that we seek for a saddle point of a cost functional. In this way, the follower control is not sensitive to a broad class of external disturbances. As far as we know, the idea of combining robustness with a Stackelberg strategy is new in literature

2016-10-19math.APmath.OC

A Verification Theorem for Stackelberg Stochastic Differential Games in Feedback Information Pattern

This paper is concerned with a Stackelberg stochastic differential game on a finite horizon in feedback information pattern. A system of parabolic partial differential equations is obtained at the level of Hamiltonian to give the verification theorem of the feedback Stackelberg equilibrium. As an example, a linear quadratic Stackelberg stochastic differential game is investigated. Riccati equations are introduced to express the feedback Stackelberg equilibrium, analytical and numerical solutions to these Riccati equations are discussed in some special cases.

2021-08-14math.OC

随机抛物型方程的Stackelberg-Nash零能控性

Stackelberg-Nash null controllability for stochastic parabolic equations

本文研究了含梯度项的随机抛物型方程的分层控制问题，采用双领导者与双跟随者的Stackelberg-Nash策略，通过Carleman估计建立能观性不等式，实现了耦合前向-后向随机系统的零能控性。

2024-07-29math.APmath.OC

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…

2023-02-04math.APmath.OC

具有内部退化性的半线性抛物型方程的分层控制

Hierarchical control for the semilinear parabolic equations with interior degeneracy

本文利用Stackelberg-Nash策略研究具有内部退化性的半线性抛物型方程的分层控制，证明Nash均衡的存在唯一性并建立新的Carleman估计以解决领导者的零能控性问题。

2023-10-30math.OC

更多相关论文收起更多论文

耦合四阶抛物方程的分层控制

Hierarchic control for the coupled fourth order parabolic equations

本文采用 Stackelberg-Nash 策略研究耦合四阶抛物系统，证明 Nash 均衡对的存在唯一性，并借助对偶与新的全局 Carleman 估计建立可观测性，从而得到零能控性。

2024-01-19math.OC

Robust Stackelberg Controllability for the Kuramoto-Sivashinsky Equation

In this article the robust Stackelberg controllability (RSC) problem is studied for a nonlinear fourth-order parabolic equation, namely, the Kuramoto-Sivashinsky equation. When three external sources are acting into the system, the RSC problem consists essentially in combining two subproblems: the first one is a saddle point problem among two sources. Such an sources are called the "follower control" and its associated "disturbance signal". This procedure corresponds to a robust control problem. The second one is a hierarchic control problem (Stackelberg strategy), which involves the third for…

2020-05-26math.APmath.OC

Hierarchical exact controllability of the fourth order parabolic equations

This paper is concerned with the application of Stackelberg-Nash strategies to control fourth order linear and semi-linear parabolic equations. We assume that the system is acted through a hierarchy of distributed controls: one main control (the leader) that is responsible for an exact controllability property; and a couple of secondary controls (the followers) that minimize two prescribed cost functionals and provides a pair of Nash equilibria for the two prescribed cost functionals. In this paper, we first prove the existence of an associated Nash equilibrium pair corresponding to a hierarch…

2022-11-01math.OC

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。

2024-05-24math.APmath.OC

Hierarchical null controllability of a semilinear degenerate parabolic equation with a gradient term

In this paper, we apply the hierarchical strategy to a semilinear weakly degenerate parabolic equation involving a gradient term. We use the Stackelberg-Nash strategy with one leader which tries to drive the solution to zero and two followers intended to solve a Nash equilibrium corresponding to a bi-objective optimal control problem. Since the system is semilinear, the functionals are not convex in general. To overcome this difficulty, we first prove the existence and uniqueness of the Nash quasi-equilibrium, which is a weaker formulation of the Nash equilibrium. Next, with additional conditi…

2022-09-26math.OC

耦合随机抛物型系统的多目标与分层控制

Multi-objective and hierarchical control for coupled stochastic parabolic systems

本文研究耦合随机抛物系统的Stackelberg-Nash零能控性，提出分层多目标控制策略，并推导新Carleman估计，为随机耦合系统控制理论提供开创性成果。

2025-01-21math.OC

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。

2025-09-10math.APmath.OC

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。

2025-09-23math.APmath.OC

一种针对随机 Kuramoto-Sivashinsky-Korteweg-de Vries 方程的分层鲁棒控制策略

A Hierarchical Robust Control Strategy for Stochastic Kuramoto--Sivashinsky--Korteweg--de Vries Equations

FST Errachidia（埃拉切迪亚高等师范学院）

本文提出一种分层鲁棒控制策略，针对随机KS-KdV方程实现零可控性，通过鞍点存在性和Carleman估计解决强耦合前向-后向随机系统分析问题。

2026-04-12math.OC

Inverse coefficient problem for Grushin-type parabolic operators

The approach to Lipschitz stability for uniformly parabolic equations introduced by Imanuvilov and Yamamoto in 1998 based on Carleman estimates, seems hard to apply to the case of Grushin-type operators studied in this paper. Indeed, such estimates are still missing for parabolic operators degenerating in the interior of the space domain. Nevertheless, we are able to prove Lipschitz stability results for inverse coefficient problems for such operators, with locally distributed measurements in arbitrary space dimension. For this purpose, we follow a strategy that combines Fourier decomposition …

2013-12-08math.APmath.OC

On the hierarchical optimal control of a chain of distributed systems

In this paper, we consider a chain of distributed systems governed by a degenerate parabolic equation, which satisfies a weak Hörmander type condition, with a control distributed over an open subdomain. In particular, we consider two objectives that we would like to accomplish. The first one being of a controllability type that consists of guaranteeing the terminal state to reach a target set starting from an initial condition; while the second one is keeping the state trajectory of the overall system close to a given reference trajectory on a finite, compact time intervals. We introduce the f…

2015-08-12math.OC

在Hilbert-贝索夫空间中使用梯度法对抛物线自由边界问题进行最优控制

Gradient Method in Hilbert-Besov Spaces for the Optimal Control of Parabolic Free Boundary Problems

Florida Institute of Technology（佛罗里达理工学院）

本文研究了逆Stefan型自由边界问题，通过梯度法在Hilbert-贝索夫空间中求解缺失的边界热流及温度和自由边界。通过预条件和正则化技术，分析了不同复杂度的模型案例。

2018-01-09cs.NAmath.APmath.NA

Optimal Controls for Forward-Backward Stochastic Differential Equations: Time-Inconsistency and Time-Consistent Solutions

This paper is concerned with an optimal control problem for a forward-backward stochastic differential equation (FBSDE, for short) with a recursive cost functional determined by a backward stochastic Volterra integral equation (BSVIE, for short). It is found that such an optimal control problem is time-inconsistent in general, even if the cost functional is reduced to a classical Bolza type one as in Peng [50], Lim-Zhou [41], and Yong [74]. Therefore, instead of finding a global optimal control (which is time-inconsistent), we will look for a time-consistent and locally optimal equilibrium str…

2022-09-19math.OCmath.PR