Open Access
Volume 28, 2022
Article Number 23
Number of page(s) 36
Published online 17 March 2022
  1. Y.V. Averboukh, A minimax approach to mean field games. Sb. Math. 206 (2015) 893–920. [CrossRef] [MathSciNet] [Google Scholar]
  2. R.A. Bandaliyev, I.G. Mamedov, M.J. Mardanov and T.K. Melikov, Fractional optimal control problem for ordinary differential equation in weighted Lebesgue spaces. Optim. Lett. 14 (2020) 1519–1532. [CrossRef] [MathSciNet] [Google Scholar]
  3. E. Bayraktar and C. Keller, Path-dependent Hamilton–Jacobi equations in infinite dimensions. J. Funct. Anal. 275 (2018) 2096–2161. [CrossRef] [MathSciNet] [Google Scholar]
  4. M. Bergounioux and L. Bourdin, Pontryagin maximum principle for general Caputo fractional optimal control problems with Bolza cost and terminal constraints. ESAIM: COCV 26 (2020) 35. [CrossRef] [EDP Sciences] [Google Scholar]
  5. A.G. Butkovskii, S.S. Postnov and E.A. Postnova, Fractional integro-differential calculus and its control-theoretical applications. II. Fractional dynamic systems: modeling and hardware implementation. Autom. Remote Control 74 (2013) 725–749. [CrossRef] [MathSciNet] [Google Scholar]
  6. M.G. Crandall, H. Ishii and P.-L. Lions, Uniqueness of viscosity solutions of Hamilton–Jacobi equations revisited. J. Math. Soc. Jpn. 39 (1987) 581–596. [CrossRef] [Google Scholar]
  7. M.G. Crandall and P.-L. Lions, Viscosity solutions of Hamilton–Jacobi equations. Trans. Amer. Math. Soc. 277 (1983) 1–42. [CrossRef] [MathSciNet] [Google Scholar]
  8. K. Diethelm, The analysis of fractional differential equations: an application-oriented exposition using differential operators of Caputo type. Lecture Notes in Mathematics, vol 2004. Springer, Berlin-Heidelberg (2010). [CrossRef] [Google Scholar]
  9. A.F. Filippov, Differential equations with discontinuous righthand sides: control systems. Math. Appl. (Soviet Ser.), vol 18. Kluwer Academic Publishers, Dordrecht, The Netherlands (1988). [Google Scholar]
  10. A. Flores-Tlacuahuac and L.T. Biegler, Optimization of fractional order dynamic chemical processing systems. Ind. Eng. Chem. Res. 53 (2014) 5110–5127. [CrossRef] [Google Scholar]
  11. M.I. Gomoyunov, Fractional derivatives of convex Lyapunov functions and control problems in fractional order systems. Fract. Calc. Appl. Anal. 21 (2018) 1238–1261. [CrossRef] [MathSciNet] [Google Scholar]
  12. M.I. Gomoyunov, Dynamic programming principle and Hamilton-Jacobi-Bellman equations for fractional-order systems. SIAM J. Control Optim. 58 (2020) 3185–3211. [CrossRef] [MathSciNet] [Google Scholar]
  13. M.I. Gomoyunov, Optimal control problems with a fixed terminal time in linear fractional-order systems. Arch. Control Sci. 30 (2020) 721–744. [MathSciNet] [Google Scholar]
  14. M.I. Gomoyunov, Solution to a zero-sum differential game with fractional dynamics via approximations. Dyn. Games Appl. 10 (2020) 417–443. [CrossRef] [MathSciNet] [Google Scholar]
  15. M.I. Gomoyunov, To the theory of differential inclusions with Caputo fractional derivatives. Diff. Equat. 56 (2020) 1387–1401. [CrossRef] [Google Scholar]
  16. M.I. Gomoyunov, On differentiability of solutions of fractional differential equations with respect to initial data. Preprint arXiv:2111.14400 (2021). [Google Scholar]
  17. M.I. Gomoyunov, N.Y. Lukoyanov and A.R. Plaksin, Path-dependent Hamilton–Jacobi equations: the minimax solutions revised. Appl. Math. Optim. 84 (2021) S1087–S1117. [CrossRef] [MathSciNet] [Google Scholar]
  18. D. Idczak and S. Walczak, On a linear-quadratic problem with Caputo derivative. Opuscula Math. 36 (2016) 49–68. [CrossRef] [MathSciNet] [Google Scholar]
  19. T. Kaczorek, Minimum energy control of fractional positive electrical circuits with bounded inputs. Circuits Syst. Signal Process. 35 (2016) 1815–1829. [CrossRef] [Google Scholar]
  20. R. Kamocki and M. Majewski, Fractional linear control systems with Caputo derivative and their optimization. Optim. Control Appl. Meth. 36 (2014) 953–967. [Google Scholar]
  21. H. Kheiri and M. Jafari, Optimal control of a fractional-order model for the HIV/AIDS epidemic. Int. J. Biomath. 11 (2018) 1850086. [CrossRef] [MathSciNet] [Google Scholar]
  22. A.A. Kilbas, H.M. Srivastava and J.J. Trujillo, Theory and applications of fractional differential equations. North-Holland Math. Stud., vol 204. Elsevier, Amsterdam (2006). [Google Scholar]
  23. A.V. Kim, Functional differential equations: application of i-smooth calculus. Math. Appl., vol 479. Kluwer Academic Publishers, Dordrecht, The Netherlands (1999). [Google Scholar]
  24. A.N. Krasovskii and N.N. Krasovskii, Control under lack of information. Systems Control Found. Appl., Birkhäuser, Boston (1995). [CrossRef] [Google Scholar]
  25. N.N. Krasovskii, On the problem of the unification of differential games. Dokl. Akad. Nauk SSSR 226 (1976) 1260–1263. [MathSciNet] [Google Scholar]
  26. N.N. Krasovskii and A.I. Subbotin, Game-theoretical control problems. Springer Ser. Soviet Math., Springer, New York (1988). [CrossRef] [Google Scholar]
  27. V.A. Kubyshkin and S.S. Postnov, Optimal control problem for a linear stationary fractional order system in the form of a problem of moments: problem setting and a study. Autom. Remote Control 75 (2014) 805–817. [CrossRef] [MathSciNet] [Google Scholar]
  28. A.B. Kurzhanskii, The existence of solutions of equations with after effect. Differ. Uravn. 6 (1970) 1800–1809 (in Russian). [Google Scholar]
  29. W. Li, S. Wang and V. Rehbock, Numerical solution of fractional optimal control. J. Optim. Theory Appl. 180 (2019) 556–573. [CrossRef] [MathSciNet] [Google Scholar]
  30. P. Lin and J. Yong, Controlled singular Volterra integral equations and Pontryagin maximum principle. SIAM J. Control Optim. 58 (2020) 136–164. [CrossRef] [MathSciNet] [Google Scholar]
  31. N.Y. Lukoyanov, Functional Hamilton–Jacobi type equations in ci-derivatives for systems with distributed delays. Nonlinear Funct. Anal. Appl. 8 (2003) 365–397. [MathSciNet] [Google Scholar]
  32. N.Y. Lukoyanov, Functional Hamilton–Jacobi type equations with ci-derivatives in control problems with hereditary information, Nonlinear Funct. Anal. Appl. 8 (2003) 535–555. [MathSciNet] [Google Scholar]
  33. N.Y. Lukoyanov, Strategies for aiming in the direction of invariant gradients. J. Appl. Math. Mech. 68 (2004) 561–574. [CrossRef] [MathSciNet] [Google Scholar]
  34. N.Y. Lukoyanov, Differential inequalities for a nonsmooth value functional in control systems with an aftereffect. Proc. Steklov Inst. Math. 255 (2006) S103–S114. [CrossRef] [Google Scholar]
  35. N.Y. Lukoyanov, On viscosity solution of functional Hamilton–Jacobi type equations for hereditary systems. Proc. Steklov Inst. Math. 259 (2007) S190–S200. [CrossRef] [Google Scholar]
  36. N.Y. Lukoyanov, Minimax and viscosity solutions in optimization problems for hereditary systems. Proc. Steklov Inst. Math. 269 (2010) S214–S225. [CrossRef] [Google Scholar]
  37. N.Y. Lukoyanov, Functional Hamilton–Jacobi equations and control problems with hereditary information. Ural Federal University Publishing, Ekaterinburg, Russia (2011) (in Russian). [Google Scholar]
  38. N.Y. Lukoyanov, M.I. Gomoyunov and A.R. Plaksin, Hamilton–Jacobi functional equations and differential games for neutral-type systems. Dokl. Math. 96 (2017) 654–657. [CrossRef] [MathSciNet] [Google Scholar]
  39. N.Y. Lukoyanov and A.R. Plaksin, Stable functionals of neutral-type dynamical systems. Proc. Steklov Inst. Math. 304 (2019) 205–218. [CrossRef] [MathSciNet] [Google Scholar]
  40. I. Matychyn and V. Onyshchenko, Optimal control of linear systems with fractional derivatives. Fract. Calc. Appl. Anal. 21 (2018) 134–150. [CrossRef] [MathSciNet] [Google Scholar]
  41. K.S. Miller and B. Ross, An introduction to the fractional calculus and fractional differential equations. A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York (1993). [Google Scholar]
  42. A.R. Plaksin, Minimax solution of functional Hamilton–Jacobi equations for neutral type systems. Differ. Equ. 55 (2019) 1475–1484. [CrossRef] [MathSciNet] [Google Scholar]
  43. I. Podlubny, Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications. Math. Sci. Engrg., vol 198. Academic Press, Inc., San Diego, CA (1999). [Google Scholar]
  44. B. Ross, S.G. Samko and E.R. Love, Functions that have no first order derivative might have fractional derivatives of all orders less than one. Real Anal. Exchange 20 (1994–1995) 140–157. [CrossRef] [MathSciNet] [Google Scholar]
  45. A.B. Salati, M. Shamsi and D.F.M. Torres, Direct transcription methods based on fractional integral approximation formulas for solving nonlinear fractional optimal control problems. Commun. Nonlinear Sci. Numer. Simul. 67 (2019) 334–350. [CrossRef] [MathSciNet] [Google Scholar]
  46. S.G. Samko, A.A. Kilbas and O.I. Marichev, Fractional integrals and derivatives: theory and applications. Gordon and Breach Science Publishers, Yverdon, Switzerland (1993). [Google Scholar]
  47. B. Sendov, Hausdorff approximations. Kluwer Academic Publishers, Dordrecht, The Netherlands (1990). [CrossRef] [Google Scholar]
  48. A.I. Subbotin, Generalized solutions of first order PDEs: the dynamical optimization perspective. Systems Control Found. Appl., Birkhäuser, Basel (1995). [CrossRef] [Google Scholar]
  49. A.I. Subbotin, Minimax solutions of first–order partial differential equations. Russ. Math. Surv. 51 (1996) 283–313. [CrossRef] [Google Scholar]
  50. R. Toledo-Hernandez, V. Rico-Ramirez, R. Rico-Martinez, S. Hernandez-Castro and U.M. Diwekar, A fractional calculus approach to the dynamic optimization of biological reactive systems. Part II: Numerical solution of fractional optimal control problems. Chem. Eng. Sci. 117 (2014) 239–247. [Google Scholar]
  51. S.S. Zeid, S. Effati and A.V. Kamyad, Approximation methods for solving fractional optimal control problems. Comp. Appl. Math. 37 (2018) 158–182. [CrossRef] [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.