Robust hierarchic control for a population dynamics model with missing birth rate

Mophou, Gisèle; Kere, Moumini; Njoukoué, Lionel Landry Djomegne

doi:10.1007/s00498-020-00260-0

Cited by 8 publications

(2 citation statements)

References 16 publications

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“…Arguing as in [8,29] while using convergences (2.59), we prove that (z, p) is a solution of (2.11)-(2.12) corresponding to the control f and also z satisfies (1.7). Furthermore, using the convergence (2.59a), we have that f satisfies (2.50).…”

Section: Observability and Null Controllabilitymentioning

confidence: 84%

Stackelberg exact controllability of a class of nonlocal parabolic equations

Landry¹,

Kenne²

2023

Preprint

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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 consists to minimize a given cost functional. The paper considers two cases: in the first case, both the leader and the follower act in the interior of the domain, and in the second case, the leader acts in the interior of the domain and the follower acts on a small part of the boundary. These results are applied to both linear and nonlinear nonlocal parabolic systems.

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Section: Observability and Null Controllabilitymentioning

confidence: 84%

Stackelberg exact controllability of a class of nonlocal parabolic equations

Landry¹,

Kenne²

2023

Preprint

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“…More recently, in [8], the authors dealt with the hierarchical exact controllability of parabolic equations with distributed and boundary controls. The same method was also applied in the context of parabolic coupled systems in [29] and [27] and mixed with robust control in [28] and [39]. The previous works have considered Dirichlet and Neumann boundary conditions.…”

mentioning

confidence: 99%

Stackelberg-Nash null controllability of heat equation with general dynamic boundary conditions

Boutaayamou¹,

Maniar²,

Oukdach³

2022

EECT

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<p style='text-indent:20px;'>This paper deals with the hierarchical control of the anisotropic heat equation with dynamic boundary conditions and drift terms. We use the Stackelberg-Nash strategy with one leader and two followers. To each fixed leader, we find a Nash equilibrium corresponding to a bi-objective optimal control problem for the followers. Then, by some new Carleman estimates, we prove a null controllability result.</p>

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