Open Access
Issue
ESAIM: COCV
Volume 29, 2023
Article Number 22
Number of page(s) 39
DOI https://doi.org/10.1051/cocv/2023011
Published online 24 March 2023
  1. A. Agrachev and Y. Sachkov, Control Theory from the Geometric Viewpoint. Encyclopaedia of Mathematical Sciences, Springer-Verlag Berlin Heidelberg (2004). [CrossRef] [Google Scholar]
  2. A. Agrachev, Y. Baryshnikov and A. Sarychev, Ensemble controllability by Lie algebraic methods. ESAIM: COCV 22 (2016) 921–938. [CrossRef] [EDP Sciences] [Google Scholar]
  3. N. Augier, U. Boscain and M. Sigalotti, Adiabatic ensemble control of a continuum of quantum systems. SIAM J. Control Optim. 56 (2018) 4045–4068. [CrossRef] [MathSciNet] [Google Scholar]
  4. K. Beauchard, J.-M. Coron and P. Rouchon, Controllability issues for continuousspectrum systems and ensemble controllability of Bloch equations. Commun. Math. Phys. 296 (2010) 525–557. [CrossRef] [Google Scholar]
  5. M. Belhadj, J. Salomon and G. Turinici, Ensemble controllability and discrimination of perturbed bilinear control systems on connected, simple, compact Lie groups. Eur. J. Control 22 (2015) 23–29. [CrossRef] [MathSciNet] [Google Scholar]
  6. P. Bettiol and N. Khalil, Necessary optimality conditions for average cost minimization problems. Discete Contin. Dyn. Syst. - B. 24 (2019) 2093–2124. [Google Scholar]
  7. B. Bonnet, C. Cipriani, M. Fornasier and H. Huang, A measure theoretical approach to the mean-field maximum principle for training NeurODEs. Nonlinear Anal. 227 (2023) 113–161. [Google Scholar]
  8. H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext, Springer New York NY (2011). [Google Scholar]
  9. R.W. Brockett, On the control of a flock by a leader. Proc. Steklov Inst. Math. 268 (2010) 49–57. [CrossRef] [MathSciNet] [Google Scholar]
  10. F. Chernousko and A. Lyubushin, Method of successive approximations for solution of optimal control problems. Opt. Control Appl. Methods 3 (1982) 101–114. [Google Scholar]
  11. F.C. Chittaro and J.P. Gauthier, Asymptotic ensemble stabilizability of the Bloch equation. Sys. Control Lett. 113 (2018) 36–44. [CrossRef] [Google Scholar]
  12. E. Cinlar, Probability and Stochastics. Graduate Texts in Mathematics, Springer-Verlag, New York (2010). [Google Scholar]
  13. J. Daleckii and M. Krein, Stability of solutions of differential equations in Banach space. Translations of Mathematical Monographs, American Mathematical Soc. (1974). [Google Scholar]
  14. G. Dal Maso, An Introduction to Γ-convergence. Progress in nonlinear differential equations and their applications. Birkhäuser, Boston, MA (1993). [Google Scholar]
  15. G. Dirr and M. Schönlein, Uniform and Lq-ensemble reachability of parameter-dependent linear systems. J. Differ. Eq. 283 (2021) 216–262. [CrossRef] [Google Scholar]
  16. S. Ethier and T. Kurtz, Markov Processes: Characterization and Convergence. Wiley series in probability and statistics. John Wiley & Sons, New York (1986). [CrossRef] [Google Scholar]
  17. J. Hale, Ordinary Differential Equations. Krieger Publishing Company (1980). [Google Scholar]
  18. P. Lambrianides, Q. Gong and D. Venturi, A new scalable algorithm for computational optimal control under uncertainty. J. Comput. Phys. 420 (2020). doi: 10.1016/j.jcp.2020.109710 [CrossRef] [MathSciNet] [Google Scholar]
  19. J.-S. Li and N. Khaneja, Control of inhomogeneous quantum ensembles, Phys. Rev. A 73 (2006) doi: 10.1103/Phys-RevA.73.030302. [Google Scholar]
  20. J.-S. Li and N. Khaneja, Ensemble control of Bloch equations. IEEE Transat. Automat. Control 54 (2009) 528–536. [CrossRef] [Google Scholar]
  21. Q. Mérigot, F. Santambrogio and C. Sarrazin, Non-asymptotic convergence bounds for Wasserstein approximation using point clouds. Adv. Neur. Inf. Process Syst. 34 (2021) 12810–12821. [Google Scholar]
  22. R. Murray and M. Palladino, A model for system uncertainty in reinforcement learning. Syst. Control Lett. 122 (2018) 24–31. [CrossRef] [Google Scholar]
  23. Y. Nesterov, Lectures on Convex Optimization. Springer Optimization, Springer Nature Switzerland AG (2018). [CrossRef] [Google Scholar]
  24. A. Pacifico, A. Pesare and M. Falcone, A new algorithm for the LQR problem with partially unknown dynamics. Vol. 13127 of Large-Scale Scientific Computing 2021. Lecture Notes in Computer Science. Springer (2022). [Google Scholar]
  25. A. Pesare, M. Palladino and M. Falcone, Convergence of the Value Function in Optimal Control Problems with Unknown Dynamics. 2021 European Control Conference (ECC) (2021), pp. 2426–2431. [CrossRef] [Google Scholar]
  26. A. Pesare, M. Palladino and M. Falcone, Convergence results for an averaged LQR problem with applications to Reinforcement Learning. Math. Control Signals Syst. 33 (2021) 379–411. [CrossRef] [Google Scholar]
  27. C. Phelps, J.O. Royset and Q. Gong, Optimal control of uncertain systems using sample average approximations. SIAM J. Control Optim. 54 (2016) 1–29. [CrossRef] [MathSciNet] [Google Scholar]
  28. J. Ruths and J.-S. Li, Optimal control of inhomogenous ensembles. IEEE Trans. Aut. Control 57 (2012) 2021–2032. [CrossRef] [Google Scholar]
  29. Y. Sakawa and Y. Shindo, On global convergence of an algorithm for optimal control. IEEE Trans. Automat. Contr. 25 (1980) 1149–1153. [CrossRef] [Google Scholar]
  30. A. Scagliotti, A gradient flow equation for optimal control problems with end-point cost. J. Dyn. Control Syst. (2022). doi: 10.1007/s10883-022-09604-2. [Google Scholar]
  31. A. Scagliotti, Deep Learning approximation of diffeomorphisms via linear-control systems. Math. Control Relat. Fields (2022). doi: 10.3934/mcrf.2022036. [Google Scholar]
  32. R. Triggiani, Controllability and observability in Banach spaces with bounded operators. SIAM J. Control 13 (1975) 462–491. [CrossRef] [MathSciNet] [Google Scholar]
  33. R.B. Vinter, Minimax optimal control. SIAM J. Control Optim. 44 (2005) 939–968. [CrossRef] [MathSciNet] [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.