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Optimal feedback control for semilinear fractional evolution equations in Banach spaces. (English) Zbl 1250.49035
Summary: In this paper, we study optimal feedback controls of a system governed by semilinear fractional evolution equations via a compact semigroup in Banach spaces. By using the Cesari property, the Fillipov theorem and extending the earlier work on fractional evolution equations, we prove the existence of feasible pairs. An existence result of optimal control pairs for the Lagrange problem is presented.
MSC:
49N35Optimal feedback synthesis
49J27Optimal control problems in abstract spaces (existence)
References:
[1]Kilbas, A. A.; Srivastava, H. M.; Trujillo, J. J.: Theory and applications of fractional differential equations, North-holland mathematics studies 204 (2006)
[2]Lakshmikantham, V.; Leela, S.; Devi, J. V.: Theory of fractional dynamic systems, (2009)
[3]Miller, K. S.; Ross, B.: An introduction to the fractional calculus and differential equations, (1993)
[4]Podlubny, I.: Fractional differential equations, (1999)
[5]Tarasov, V. E.: Fractional dynamics: application of fractional calculus to dynamics of particles, fields and media, (2010)
[6]Agarwal, R. P.; Benchohra, M.; Hamani, S.: A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions, Acta appl. Math. 109, 973-1033 (2010) · Zbl 1198.26004 · doi:10.1007/s10440-008-9356-6
[7]Agarwal, R. P.; Belmekki, M.; Benchohra, M.: A survey on semilinear differential equations and inclusions involving Riemann–Liouville fractional derivative, Adv. differential equations, 47 (2009) · Zbl 1182.34103 · doi:10.1155/2009/981728
[8]Balachandran, K.; Park, J. Y.: Controllability of fractional integrodifferential systems in Banach spaces, Nonlinear anal. 3, 363-367 (2009) · Zbl 1175.93028 · doi:10.1016/j.nahs.2009.01.014
[9]Benchohra, M.; Henderson, J.; Ntouyas, S. K.; Ouahab, A.: Existence results for fractional order functional differential equations with infinite delay, J. math. Anal. appl. 338, 1340-1350 (2008) · Zbl 1209.34096 · doi:10.1016/j.jmaa.2007.06.021
[10]Chang, Y. K.; Kavitha, V.; Arjunan, M. M.: Existence and uniqueness of mild solutions to a semilinear integrodifferential equation of fractional order, Nonlinear anal. 71, 5551-5559 (2009) · Zbl 1179.45010 · doi:10.1016/j.na.2009.04.058
[11]El-Borai, M. M.: Semigroup and some nonlinear fractional differential equations, Appl. math. Comput. 149, 823-831 (2004) · Zbl 1046.34079 · doi:10.1016/S0096-3003(03)00188-7
[12]El-Borai, M. M.: The fundamental solutions for fractional evolution equations of parabolic type, J. appl. Math. stoch. Anal. 3, 197-211 (2004) · Zbl 1081.34053 · doi:10.1155/S1048953304311020
[13]Henderson, J.; Ouahab, A.: Fractional functional differential inclusions with finite delay, Nonlinear anal. 70, 2091-2105 (2009) · Zbl 1159.34010 · doi:10.1016/j.na.2008.02.111
[14]Hernández, E.; O’regan, D.; Balachandran, K.: On recent developments in the theory of abstract differential equations with fractional derivatives, Nonlinear anal. 73, 3462-3471 (2010) · Zbl 1229.34004 · doi:10.1016/j.na.2010.07.035
[15]Hu, L.; Ren, Y.; Sakthivel, R.: Existence and uniqueness of mild solutions for semilinear integro-differential equations of fractional order with nonlocal initial conditions and delays, Semigroup forum 79, 507-514 (2009) · Zbl 1184.45006 · doi:10.1007/s00233-009-9164-y
[16]Jaradat, O. K.; Al-Omari, A.; Momani, S.: Existence of the mild solution for fractional semilinear initial value problems, Nonlinear anal. 69, 3153-3159 (2008) · Zbl 1160.34300 · doi:10.1016/j.na.2007.09.008
[17]N’guérékata, G. M.: A Cauchy problem for some fractional abstract differential equation with nonlocal conditions, Nonlinear anal. 70, 1873-1876 (2009) · Zbl 1166.34320 · doi:10.1016/j.na.2008.02.087
[18]Mophou, G. M.; N’guérékata, G. M.: Existence of mild solutions of some semilinear neutral fractional functional evolution equations with infinite delay, Appl. math. Comput. 216, 61-69 (2010) · Zbl 1191.34098 · doi:10.1016/j.amc.2009.12.062
[19]Wang, J.; Zhou, Y.: A class of fractional evolution equations and optimal controls, Nonlinear anal. 12, 262-272 (2011) · Zbl 1214.34010 · doi:10.1016/j.nonrwa.2010.06.013
[20]Wang, J.; Zhou, Y.: Study of an approximation process of time optimal control for fractional evolution systems in Banach spaces, Adv. differential equations 2011 (2011) · Zbl 1222.49006 · doi:10.1155/2011/385324
[21]Wang, J.; Zhou, Y.; Wei, W.; Xu, H.: Nonlocal problems for fractional integrodifferential equations via fractional operators and optimal controls, Comput. math. Appl. 62, 1427-1441 (2011) · Zbl 1228.45015 · doi:10.1016/j.camwa.2011.02.040
[22]Wang, J.; Wei, W.; Zhou, Y.: Fractional finite time delay evolution systems and optimal controls in infinite dimensional spaces, J. dyn. Control syst. 17, 515-535 (2011)
[23]Zhou, Y.; Jiao, F.: Nonlocal Cauchy problem for fractional evolution equations, Nonlinear anal. 11, 4465-4475 (2010)
[24]Zhou, Y.; Jiao, F.: Existence of mild solutions for fractional neutral evolution equations, Comput. math. Appl. 59, 1063-1077 (2010) · Zbl 1189.34154 · doi:10.1016/j.camwa.2009.06.026
[25]Franklin, G. F.; Powell, J. D.; Emami-Naeini, A.: Feedback control of dynamic systems, (1986) · Zbl 0615.93001
[26]Mees, A. I.: Dynamics of feedback systems, (1981) · Zbl 0454.93003
[27]Kamenskii, M. I.; Nistri, P.; Obukhovskii, V. V.; Zecca, P.: Optimal feedback control for a semilinear evolution equation, J. optim. Theory appl. 82, 503-517 (1994) · Zbl 0817.49002 · doi:10.1007/BF02192215
[28]Wei, W.; Xiang, X.: Optimal feedback control for a class of nonlinear impulsive evolution equations, Chinese J. Engrg. math. 23, 333-342 (2006) · Zbl 1140.49026
[29]Li, X.; Yong, J.: Optimal control theory for infinite dimensional systems, (1995)
[30]Aubin, J. P.; Frankowska, H.: Set valued analysis, (1990)