PDE-constrained optimal control of a leader-follower opinion formation model
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916944125362176 |
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| author | Düring, Bertram Wright, Oliver |
| author_facet | Düring, Bertram Wright, Oliver |
| contents | We consider the PDE-constrained optimal control of a leader-follower kinetic opinion formation model, with a Fokker-Planck-type system of partial differential equations as a state constraint. We derive the Boltzmann-type and Fokker-Planck-type systems of equations associated with the controlled leader-follower opinion formation model. In a function space setting we derive first-order optimality conditions associated with the PDE-constrained optimal control problem, yielding an optimality system of coupled nonlinear partial differential equations. We employ a gradient-type sweeping algorithm to numerically attack the optimality system obtained from the first-order optimality conditions. We present the results from a finite elements based simulation for different types of interactions and cost functionals. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_21674 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | PDE-constrained optimal control of a leader-follower opinion formation model Düring, Bertram Wright, Oliver Optimization and Control Physics and Society 49M41, 91D30, 35Q93 We consider the PDE-constrained optimal control of a leader-follower kinetic opinion formation model, with a Fokker-Planck-type system of partial differential equations as a state constraint. We derive the Boltzmann-type and Fokker-Planck-type systems of equations associated with the controlled leader-follower opinion formation model. In a function space setting we derive first-order optimality conditions associated with the PDE-constrained optimal control problem, yielding an optimality system of coupled nonlinear partial differential equations. We employ a gradient-type sweeping algorithm to numerically attack the optimality system obtained from the first-order optimality conditions. We present the results from a finite elements based simulation for different types of interactions and cost functionals. |
| title | PDE-constrained optimal control of a leader-follower opinion formation model |
| topic | Optimization and Control Physics and Society 49M41, 91D30, 35Q93 |
| url | https://arxiv.org/abs/2508.21674 |