Selective model-predictive control for flocking systems

1. C. K. Hemelrijk and H. Hildenbrandt, Schools of _sh and ocks of birds: their shape and internal structure by self-organization, Mathematical Models and Methods in Applied Sciences, vol. 2, no. 6, pp. 726{737, 2012.10.1098/rsfs.2012.0025349912224312726Search in Google Scholar

2. S. Camazine, J. Deneubourg, N. R. Franks, J. Sneyd, G. Theraulaz, and E. Bonabeau, Self- Organization in Biological Systems. Princeton: Princeton University Press, 2001.Search in Google Scholar

3. T. Vicsek and A. Zafeiris, Collective motion, Physics Reports, vol. 517, no. 3{4, pp. 71{140, 2012.10.1016/j.physrep.2012.03.004Search in Google Scholar

4. D. Helbing and P. Moln_ar, Social force model for pedestrian dynamics, Physical Review E, vol. 51, no. 5, pp. 4282{4286, 1995.10.1103/PhysRevE.51.4282Search in Google Scholar

5. J. A. Ca~nizo, J. A. Carrillo, and J. Rosado, A well-posedness theory in measures for some kineticmodels of collective motion, Mathematical Models and Methods in Applied Sciences, vol. 21, no. 03, pp. 515{539, 2011.10.1142/S0218202511005131Search in Google Scholar

6. S. Motsch and E. Tadmor, Heterophilious dynamics enhances consensus, SIAM Review, vol. 56, no. 4, pp. 577{621, 2014.10.1137/120901866Search in Google Scholar

7. E. Cristiani, B. Piccoli, and A. Tosin, Multiscale modeling of pedestrian dynamics, vol. 12 of Modeling, Simulation and Applications. Cham: Springer, 2014.10.1007/978-3-319-06620-2Search in Google Scholar

8. L. Pareschi and G. Toscani, Interacting Multiagent Systems. Kinetic Equations & Monte Carlo Meth-ods. New York: Oxford University Press, 2013.Search in Google Scholar

9. V. Gazi and K. Passino, Stability analysis of swarms, IEEE Transactions on Automatic Control, vol. 48, no. 4, pp. 692{697, 2003.10.1109/TAC.2003.809765Search in Google Scholar

10. M. Aureli, F. Fiorilli, and M. Portraits, Portraits of self-organization in fish schools interacting with robots, Physica D: Nonlinear Phenomena, vol. 241, no. 9, pp. 908{920, 2012.10.1016/j.physd.2012.02.005Search in Google Scholar

11. C. W. Reynolds, Flocks, herds and schools: a distributed behavioral model, SIGGRAPH ComputerGraphics, vol. 21, no. 4, pp. 25{34, 1987.10.1145/37402.37406Search in Google Scholar

12. J. Kennedy and R. Eberhart, Particle swarm optimization, in Proceedings of ICNN'95 International Conference on Neural Networks, vol. 4, pp. 1942{1948, New York: IEEE, 1995.Search in Google Scholar

13. E. Bonabeau, M. Dorigo, and G. Theraulaz, Swarm Intelligence: From Natural to Artiffcial Systems. New York: Oxford University Press, 1999.10.1093/oso/9780195131581.001.0001Search in Google Scholar

14. J. A. Carrillo, Y.-P. Choi, C. Totzeck, and O. Tse, An analytical framework for a consensus-basedglobal optimization method, ArXiv e-prints, January 2016.Search in Google Scholar

15. M. Brambilla, E. Ferrante, M. Birattari, and M. Dorigo, Swarm robotics: a review from the swarmengineering perspective, Swarm Intelligence, 2013.10.1007/s11721-012-0075-2Search in Google Scholar

16. G. Albi, M. Herty, and L. Pareschi, Kinetic description of optimal control problems in consensus, Communications in Mathematical Sciences, vol. 13, no. 6, pp. 1407{1429, 2015.10.4310/CMS.2015.v13.n6.a3Search in Google Scholar

17. M. Bongini, D. Kalise, , and M. Fornasier, (Un)conditional consensus emergence under perturbed anddecentralized feedback controls. NETCO 2014 | New Trends in Optimal Control, June 2014.Search in Google Scholar

18. M. Bongini and M. Fornasier, Sparse stabilization of dynamical systems driven by attraction andavoidance forces, Networks & Heterogeneous Media, vol. 9, no. 1, pp. 1{31, 2014.10.3934/nhm.2014.9.1Search in Google Scholar

19. A. Borzi and S. Wongkaew, Modeling and control through leadership of a refined flocking system, Mathematical Models and Methods in Applied Sciences, vol. 25, no. 02, pp. 255{282, 2015.10.1142/S0218202515500098Search in Google Scholar

20. M. Caponigro, M. Fornasier, B. Piccoli, and E. Trelat, Sparse stabilization and control of alignmentmodel, Mathematical Models and Methods in Applied Sciences, vol. 25, no. 03, pp. 521{564, 2015.10.1142/S0218202515400059Search in Google Scholar

21. N. Moshtagh and A. Jadbabaie, Distributed geodesic control laws for ocking of nonholonomic agents, IEEE Transactions on Automatic Control, vol. 52, no. 4, pp. 681{686, 2007.10.1109/TAC.2007.894528Search in Google Scholar

22. N. Moshtagh, N. Michael, A. Jadbabaie, and K. Daniilidis, Vision-based, distributed control laws formotion coordination of nonholonomic robots, IEEE Transactions on Robotics, vol. 25, no. 4, pp. 851{860, 2009.10.1109/TRO.2009.2022439Search in Google Scholar

23. F. Cucker and S. Smale, Emergent behavior in ocks, IEEE Transactions on Automatic Control, 24. S. Y. Ha, T. Ha, and J. Kim, Emergent behavior of a cucker-smale type particle model with nonlinearvelocity couplings, IEEE Transactions on Automatic Control, vol. 55, no. 7, pp. 1679{1683, 2010.10.1109/TAC.2010.2046113Search in Google Scholar

25. R. Olfati-Saber and R. M. Murray, Consensus problems in networks of agents with switching topologyand time-delays, IEEE Transactions on Automatic Control, vol. 49, no. 9, pp. 1520{1533, 2004.10.1109/TAC.2004.834113Search in Google Scholar

26. M. Fornasier, B. Piccoli, and F. Rossi, Sparse mean-field optimal control, Philosophical Transactions ofthe Roual Society A Mathematical Physycal and Engineering Sciences, vol. 372, no. 2028, p. 20140138, 2014.10.1098/rsta.2013.0400Search in Google Scholar

27. G. Albi, M. Bongini, E. Cristiani, and D. Kalise, Invisible control of self-organizing agents leaving unknown environments, SIAM Journal on Applied Mathematics, vol. 76, no. 4, pp. 1683{1710, 2016.10.1137/15M1017016Search in Google Scholar

28. M. Caponigro, B. Piccoli, F. Rossi, and E. Trelat, Mean-field sparse Jurdjevic{Quinn control, Math-ematical Models and Methods in Applied Sciences, vol. 27, no. 07, pp. 1223{1253, 2017.10.1142/S0218202517400140Search in Google Scholar

29. P. Degond, J.-G. Liu, and C. Ringhofer, Large-scale dynamics of mean-field games driven by localnash equilibria, Journal of Nonlinear Science, vol. 24, no. 1, pp. 93{115, 2014.10.1007/s00332-013-9185-2Search in Google Scholar

30. P. Degond, M. Herty, and J.-G. Liu, Meanfield games and model predictive control, Communicationsin Mathematical Sciences, vol. 15, no. 5, pp. 1403{1422, 2017.10.4310/CMS.2017.v15.n5.a9Search in Google Scholar

31. A. Bensoussan, J. Frehse, and P. Yam, Swarm Mean Field Games and Mean Field Type ControlTheory. SpringerBriefs in Mathematics, New York: Springer, 2013.10.1007/978-1-4614-8508-7Search in Google Scholar

32. E. D. Sontag, Mathematical Control Theory, vol. 6 of Texts in Applied Mathematics. New York: Springer, second ed., 1998.10.1007/978-1-4612-0577-7Search in Google Scholar

33. D. Q. Mayne and H. Michalska, Receding horizon control of nonlinear systems, IEEE Transactionson Automatic Control, vol. 35, no. 7, pp. 814{824, 1990.10.1109/9.57020Search in Google Scholar

34. G. Albi, L. Pareschi, and M. Zanella, Boltzmann type control of opinion consensus through leaders, Philosophical Transactions of the Roual Society A Mathematical Physycal and Engineering Sciences, vol. 372, no. 2028, p. 20140138, 2014.10.1098/rsta.2014.0138Search in Google Scholar

35. J. A. Carrillo, M. Fornasier, G. Toscani, and F. Vecil, Particle, kinetic, and hydrodynamic modelsof swarming, in Mathematical modeling of collective behavior in socio-economic and life sciences (G. Naldi, L. Pareschi, and G. Toscani, eds.), vol. 496 of Mathematics Modeling and Simulation inScience, Engineering and Technology, pp. 297{336, Boston: Birkhauser, 2010.10.1007/978-0-8176-4946-3_12Search in Google Scholar

36. J. A. Carrillo, Y.-P. Choi, M. Hauray, and S. Salem, Mean-field limit for collective behavior models with sharp sensitivity regions, Journal of the European Mathematical Society, 2018. To appear.10.4171/JEMS/832Search in Google Scholar

37. M. Fornasier and F. Solombrino, Mean-field optimal control, ESAIM Control, Optimisation and Cal-culus of Variations, vol. 20, no. 4, pp. 1123{1152, 2014.10.1051/cocv/2014009Search in Google Scholar

38. E. Camacho and C. Bordons, Model Predictive Control. London: Springer, second ed., 2007.10.1007/978-0-85729-398-5Search in Google Scholar

39. J. Haskovec, Flocking dynamics and mean-field limit in the Cucker-Smale-type model with topologicalinteractions, Physica D: Nonlinear Phenomena, vol. 261, pp. 42{51, 2013.10.1016/j.physd.2013.06.006Search in Google Scholar

40. G. Albi and L. Pareschi, Binary interaction algorithms for the simulation of ocking and swarmingdynamics, Multiscale Modeling & Simulation, vol. 11, no. 1, pp. 1{29, 2013.10.1137/120868748Search in Google Scholar

41. B. Piccoli, F. Rossi, and E. Tr_elat, Control to ocking of the kinetic cucker{smale model, SIAMJournal on Mathematical Analysis, vol. 47, no. 6, pp. 4685{4719, 2015.10.1137/140996501Search in Google Scholar