A Note Concerning to Optimal Feedback Control for Caputo Fractional Neutral Stochastic Evolution Systems

• S. Vivek ^[1] ; V. Vijayakumar ^[1]
  1. [1] Vellore Institute of Technology
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 22, Nº 4, 2023
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • In this paper, we discuss the optimal feedback control for a system of semilinear neutral stochastic integrodifferential equations in Hilbert space. Using the fixed-point technique, fractional calculus, and stochastic theory we obtained the existence result for the given feedback control system. The existence of feasible pairs were employed by involving Filippov theorem and the Cesari property. Moreover, optimal feedback control pairs are presented under sufficient conditions and also, we extend the discussion to the given system with nonlocal conditions. Finally, an example is given to validate our findings.

• Referencias bibliográficas
  • 1. Aubin, J.P., Frankowska, H.: Set Valued Analysis. Berkhauser, Boston (1990)
  • 2. Balasubramaniam, P., Tamilalagan, P.: Approximate controllability of a class of fractional neutral stochastic integro-differential inclusions...
  • 3. Balakrishnan, A.V.: Optimal control problems in Banach spaces, Journal of the Society for Industrial and Applied Mathematics, Series A....
  • 4. Byszewski, L.: Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem. J. Math. Anal....
  • 5. Byszewski, L., Akca, H.: On a mild solution of a semilinear functional–differential evolution nonlocal problem. J. Appl. Math. Stoch. Anal....
  • 6. Ceng, L.C., Liu, Z., Yao, J.C., Yao, Y.: Optimal control of feedback control systems governed by systems of evolution hemivariational inequalities....
  • 7. Dineshkumar, C., Nisar, K.S., Udhayakumar, R., Vijayakumar, V.: A discussion on approximate controllability of Sobolev-type Hilfer neutral...
  • 8. Dineshkumar, C., Udhayakumar, R., Vijayakumar, V., Shukla, A., Nisar, K.S.: New discussion regarding approximate controllability for Sobolev-type...
  • 9. Dineshkumar, C., Joo, Y.H.: A note concerning to approximate controllability of Atangana–Baleanu fractional neutral stochastic integro-differential...
  • 10. Dineshkumar, C., Udhayakumar, R.: Results on approximate controllability of fractional stochastic Sobolev-type Volterra–Fredholm integro-differential...
  • 11. Franklin, G.F., Powell, J.D., Emami-Naeini, A.: Feedback Control of Dynamic Systems. AddisonWesley, Boston (1986)
  • 12. Fu, X.: Approximate controllability for neutral impulsive differential inclusions with nonlocal conditions. J. Dyn. Control Syst. 17(3),...
  • 13. Guendouzi, T., Bousmaha, L.: Approximate controllability of fractional neutral stochastic functional integro-differential inclusions with...
  • 14. Hao, X., Liub, L., Wu, Y.: Mild solutions of impulsive semilinear neutral evolution equations in Banach spaces. J. Nonlinear Sci. Appl....
  • 15. Haslinger, J., Panagiotopoulos, P.D.: Optimal control of systems governed by hemivariational inequalities. Exist. Approx. Results Nonlinear...
  • 16. Huang, Y., Liu, Z., Zeng, B.: Optimal control of feedback control systems governed by hemivariational inequalities. Comput. Math. Appl....
  • 17. Jingyun, L.V., Shang, J., He, Y.: Optimal feedback control for a class of fractional integrodifferential equations of mixed type in Banach...
  • 18. Johnson, M., Vijayakumar, V.: Optimal control results for Sobolev-type fractional stochastic Volterra– Fredholm integrodifferential systems...
  • 19. Kamenskii, M.I., Nistri, P., Obukhovskii, V.V., Zecca, P.: Optimal feedback control for a semilinear evolution equation. J. Optim. Theory...
  • 20. Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and applications of fractional differential equations. In: North-Holland Mathematics...
  • 21. Klamka, J.: Stochastic controllability of systems with variable delay in control. Bull. Polish Acad. Sci. Tech. Sci. 56, 279–284 (2008)
  • 22. Kumar, S.: Mild solution and fractional optimal control of semilinear system with fixed delay. J. Optim. Theory Appl. 174, 108–121 (2017)
  • 23. Kumar, V., Debbouche, A., Nieto, J.J.: Existence, stability and controllability results for a class of switched evolution system with...
  • 24. Kumar, V., Djemai, M.: Existence, stability and controllability of piecewise impulsive dynamic systems on arbitrary time domain. Appl....
  • 25. Kumar, V., Kostic, M., Pinto, M.: Controllability results for fractional neutral differential systems with non-instantaneous impulses....
  • 26. Kumar, V., Kostic, M., Tridane, A., Debbouche, A.: Controllability of switched Hilfer neutral fractional dynamic systems with impulses....
  • 27. Kumar, V., Malik, M.: Existence, stability and controllability results of fractional dynamic system on time scales with application to...
  • 28. Kumar, V., Malik, M.: Stability and controllability results of evolution system with impulsive condition on time scales. Differ. Equ....
  • 29. Liu, Z., Li, X., Zeng, B.: Optimal feedback control for fractional neutral dynamical systems. Optimization 67(5), 549–564 (2018)
  • 30. Liu, Z., Migorski, S., Zeng, B.: Optimal feedback control and controllability for hyperbolic evolution inclusions of Clarke’s subdifferential...
  • 31. Liang, L., Liu, Z., Zhao, J.: A class of delay evolution hemivariational inequalities and optimal feedback controls. Topol. Methods Nonlinear...
  • 32. Li, X., Yong, J.: Optimal Control Theory for Infinite Dimensional Systems. Birkhauser, Boston (1995)
  • 33. Moustapha, D., Diop, M.A., Ezzinbi, K.: Optimal feedback control law for some stochastic integrodifferential equations on Hilbert spaces....
  • 34. Migorski, S., Ochal, A.: Optimal control of parabolic hemivariational inequalities. J. Global Optim. 17, 285–300 (2000)
  • 35. Mees, A.I.: Dynamics of Feedback Systems. Wiley, New York (1981)
  • 36. Nakagiri, S.I.: Optimal control of linear retarded systems in Banach spaces. J. Math. Anal. Appl. 120(1), 169–210 (1986)
  • 37. Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego (1999)
  • 38. Park, J.Y., Park, S.H.: Optimal control problems for anti-periodic quasi-linear hemivariational inequalities. Opt. Control Appl. Methods...
  • 39. Park, J.Y., Park, S.H.: Existence of solutions and optimal control problems for hyperbolic hemivariational inequalities. Anziam J. 47,...
  • 40. Pazy, A.: Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer, New York (1983)
  • 41. Sakthivel, R., Ganesh, R., Suganya, S.: Approximate controllability of fractional neutral stochastic system with infinite delay. Rep....
  • 42. Shengda, Z., Papageorgiou, N.S., Radulescu, V.D.: Nonsmooth dynamical systems: From the existence of solutions to optimal and feedback...
  • 43. Shukla, A., Sukavanam, N., Pandey, D.N.: Controllability of semilinear stochastic control system with finite delay. IMA J. Math. Control....
  • 44. Shukla, A., Sukavanam, N., Pandey, D.N., Arora, U.: Approximate controllability of second-order semilinear control system. Circuit Syst....
  • 45. Shukla, A., Sukavanam, N., Pandey, D.N.: Complete controllability of semi-linear stochastic system with delay. Rendiconti del Circolo...
  • 46. Shukla, A., Patel, R.: Existence and optimal control results for second-order semilinear system in Hilbert spaces. Circuits Syst. Signal...
  • 47. Shukla, A., Sukavanam, N., Pandey, D.N.: Approximate controllability of semilinear stochastic control system with nonlocal conditions....
  • 48. Shukla, A., Sukavanam, N., Pandey, D.N.: Approximate controllability of semilinear fractional control systems of order α ∈ (1, 2]. SIAM...
  • 49. Shukla, A., Sukavanam, N.: Interior approximate controllability of second order semilinear control systems. Int. J. Control 1, 2–34 (2022)
  • 50. Sobczyk, K.: Stochastic Differential Equations with Applications to Physics and Engineering. Kluwer, London (1991)
  • 51. Vijayakumar, V.: Approximate controllability for a class of second-order stochastic evolution inclusions of Clarke’s subdifferential type....
  • 52. Wang, J., Zhou, Y.: A class of fractional evolution equations and optimal controls. Nonlinear Anal. 12, 262–272 (2011)
  • 53. Wang, J., Zhou, Y., Wei, W., Xu, H.: Nonlocal problems for fractional integrodifferential equations via fractional operators and optimal...
  • 54. Wei, W., Xiang, X.: Optimal feedback control for a class of nonlinear impulsive evolution equations. Chin. J. Eng. Math. 23, 333–342 (2006)
  • 55. Jiang, Y.: Optimal feedback control problems driven by fractional evolution hemivariational inequalities. Math. Methods Appl. Sci. 41(11),...
  • 56. Yong, H., Liu, Z., Zeng, B.: Optimal control of feedback control systems governed by hemivariational inequalities. Comput. Math. Appl....
  • 57. Zang, Y., Li, J.: Approximate controllability of fractional impulsive neutral stochastic differential equations with nonlocal conditions....
  • 58. Zhou, Y.: Basic Theory of Fractional Differential Equations. World Scientific, Singapore (2014)
  • 59. Zhou, Y., Jiao, F.: Existence of mild solutions for fractional neutral evolution equations. Comput. Math. Appl. 59, 1063–1077 (2010)