EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 31 (2025) ESAIM: COCV, 31 (2025) 37 References
Open Access
Issue
ESAIM: COCV
Volume 31, 2025
Article Number 37
Number of page(s) 50
DOI https://doi.org/10.1051/cocv/2025025
Published online 08 April 2025
  1. F. Bullo, J. Cortes and S. Martines, Distributed Control of Robotic Networks. Applied Mathematics. Princeton University Press (2009). [CrossRef] [Google Scholar]
  2. F. Cucker and S. Smale, On the mathematics of emergence. Japanese J. Math. 2 (2007) 197–227. [Google Scholar]
  3. M. Ballerini, N. Cabibbo, R. Candelier, A. Cavagna, E. Cisbani, I. Giardina, V. Lecomte, A. Orlandi, G. Parisi, A. Procaccini, M. Viale and V. Zdravkovic, Interaction ruling animal collective behavior depends on topological rather than metric distance: Evidence from a field study. Proc. Natl. Acad. Sci. U.S.A. 105 (2008) 1232–1237. [Google Scholar]
  4. N. Bellomo, M.A. Herrero and A. Tosin, On the dynamics of social conflicts: looking for the black swan. Kinetic Related Models 6 (2013) 459–479. [CrossRef] [MathSciNet] [Google Scholar]
  5. E. Cristiani, B. Piccoli and A. Tosin, Multiscale Modeling of Pedestrian Dynamics, Vol. 12. Springer (2014). [CrossRef] [Google Scholar]
  6. S. Camazine, J.-L. Deneubourg, N.R. Franks, J. Sneyd, G. Theraulaz and E. Bonabeau, Self-organization in Biological Systems. Princeton Studies in Complexity, Princeton University Press, Princeton, NJ (2003). Reprint of the 2001 original. [Google Scholar]
  7. E.F. Keller and L.A. Segel, Initiation of slime mold aggregation viewed as an instability. J. Theoret. Biol. 26 (1970) 399–415. [Google Scholar]
  8. Y.-L. Chuang, Y.R. Huang, M.R. D’Orsogna and A. Bertozzi, Multi-vehicle flocking: Scalability of cooperative control algorithms using pairwise potentials. Proceedings 2007 IEEE International Conference on Robotics and Automation (2007) 2292–2299. [CrossRef] [Google Scholar]
  9. M. Bongini and G. Buttazzo, Optimal control problems in transport dynamics. Math. Models Methods Appl. Sci. 27 (2017) 427–451. [Google Scholar]
  10. G. Albi, M. Bongini, E. Cristiani and D. Kalise, Invisible control of self-organizing agents leaving unknown environments. SIAM J. Appl. Math. 76 (2016) 1683–1710. [Google Scholar]
  11. G. Albi, L. Pareschi and M. Zanella, Boltzmann type control of opinion consensus through leaders. Proc. Roy. Soc. A. 372 (2014). [Google Scholar]
  12. B. Piccoli, F. Rossi and E. Trelat, Control to flocking of the kinetic Cucker-Smale model. SIAM J. Math. Anal. 47 (2015) 4685–4719. [Google Scholar]
  13. A. Muntean, J. Rademacher and A. Zagaris, Macroscopic and Large Scale Phenomena: Coarse Graining, Mean Field Limits and Ergodicity. Springer (2016). [CrossRef] [Google Scholar]
  14. Y.-P. Choi, J.A. Carrillo and M. Hauray, The derivation of swarming models: mean-field limit and Wasserstein distances, in Collective Dynamics from Bacteria to Crowds, CISM International Centre for Mechanical Sciences, Vol. 553. Springer (2014) 1–46. [Google Scholar]
  15. G. Cavagnari, S. Lisini, C. Orrieri and G. Savare, Lagrangian, Eulerian and Kantorovich formulations of multi-agent optimal control problems: equivalence and gamma-convergence. J. Differ. Equ. 322 (2022) 268–364. [Google Scholar]
  16. M. Fornasier, S. Lisini, C. Orrieri and G. Savare, Mean-field optimal control as gamma-limit of finite agent controls. European J. Appl. Math. 30 (2019) 1153–1186. [Google Scholar]
  17. M. Fornasier and F. Solombrino, Mean-field optimal control. ESAIM Control Optim. Calc. Var. 20 (2014) 1123–1152. [Google Scholar]
  18. M. Bongini, M. Fornasier, F. Rossi and F. Solombrino, Mean field Pontryagin Maximum Principle. J. Optim. Theory Appl. 175 (2017) 1–38. [Google Scholar]
  19. B. Bonnet, A Pontryagin Maximum Principle in Wasserstein spaces for constrained optimal control problems. ESAIM: Control Optim. Calc. Var. 25 (2019) article no. 52. [Google Scholar]
  20. B. Bonnet and H. Frankowska, Necessary optimality conditions for optimal control problems in Wasserstein spaces. Appl. Math. Optim. 84 (2021) 1281–1330. [Google Scholar]
  21. B. Bonnet and F. Rossi, The Pontryagin Maximum Principle in the Wasserstein space. Calc. Var. Part. Differ. Equ. 58 (2019) Paper No. 11. [Google Scholar]
  22. M. Burger, L.M. Kreusser and C. Totzeck, Mean-field optimal control for biological pattern formation. ESAIM Control Optim. Calc. Var. 27 (2021) article no. 40. [Google Scholar]
  23. M. Burger, R. Pinnau, C. Totzeck and O. Tse, Mean-field optimal control and optimality conditions in the space of probability measures. SIAM J. Control Optim. 59 (2021). [Google Scholar]
  24. R. Carmona and F. Delarue, Forward-backward stochastic differential equations and controlled McKean-Vlasov dynamics. Ann. Probab. 43 (2015) 2647–2700. [Google Scholar]
  25. N. Pogodaev and M. Saritsyn, Impulsive control of nonlocal transport equation. J. Differ. Equ. 269 (2020) 3585–3623. [Google Scholar]
  26. L. Ambrosio, M. Fornasier, M. Morandotti and F. Savare, Spatially inhomogeneous evolutionary games. Commun. Pure Appl. Math. 74 (2021) 1353–1402. [Google Scholar]
  27. S. Almi, C. D’Eramo, M. Morandotti and F. Solombrino, Mean-field limits for entropic multi-population dynamical systems. Milan J. Math. 91 (2023) 175–212. [Google Scholar]
  28. S. Almi, M. Morandotti and F. Solombrino, A multi-step Lagrangian scheme for spatially inhomogeneous evolutionary games. J. Evol. Equ. 21 (2021) 2691–2733. [Google Scholar]
  29. M. Morandotti and F. Solombrino, Mean-field analysis of multipopulation dynamics with label switching. SIAM J. Math. Anal. 52 (2020) 1427–1462. [Google Scholar]
  30. G. Albi, S. Almi, M. Morandotti and F. Solombrino, Mean-field selective optimal control via transient leadership. Appl. Math. Optim. 85 (2022) Paper No. 9. [Google Scholar]
  31. H. Brezis, Operateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert. North-Holland/American Elsevier Publishing, Amsterdam/New York (1973). [Google Scholar]
  32. M. Bonafini, M. Fornasier, and B. Schmitzer, Data-driven entropic spatially inhomogeneous evolutionary games. European J. Appl. Math. 34 (2023) 106–159. [Google Scholar]
  33. B. Bonnet and H. Frankowska, Differential inclusions in Wasserstein spaces: the Cauchy-Lipschitz framework. J. Differ. Equ. 271 (2021) 594–637. [Google Scholar]
  34. R. Bonalli and B. Bonnet, First-order Pontryagin maximum principle for risk-averse stochastic optimal control problems. SIAM J. Control Optim. 61 (2023) 1881–1909. [Google Scholar]
  35. B. Bonnet and F. Rossi, Intrinsic Lipschitz regularity of mean-field optimal controls. SIAM J. Control Optim. 59 (2021) 2011–2046. [Google Scholar]
  36. L. Ambrosio, N. Gigli and G. Savare, Gradient Flows in Metric Spaces and in the Space of Probability Measures, 2nd edn. Lectures in Mathematics ETH Zürich. Birkhäuser Verlag, Basel (2008). [Google Scholar]
  37. I.A. Shvartsman, New approximation method in the proof of the Maximum Principle for nonsmooth optimal control problems with state constraints. J. Math. Anal. Appl. 326 (2007) 974–1000. [Google Scholar]
  38. J. Maas, Gradient flows of the entropy for finite Markov chains. J. Funct. Anal. 261 (2011) 2250–2292. [Google Scholar]
  39. A. Mielke, Geodesic convexity of the relative entropy in reversible Markov chains. Calc. Var. Part. Differ. Equ. 48 (2013) 1–31. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.