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Approximate controllability of nonlinear impulsive differential systems. (English) Zbl 1141.93015
Summary: Many practical systems in physical and biological sciences have impulsive dynamical behaviours during the evolution process which can be modeled by impulsive differential equations. This paper studies the approximate controllability issue for nonlinear impulsive differential and neutral functional differential equations in Hilbert spaces. Based on the semigroup theory and fixed point approach, sufficient conditions for approximate controllability of impulsive differential and neutral functional differential equations are established. Finally, two examples are presented to illustrate the utility of the proposed result. The results improve some recent results.

MSC:
93B05Controllability
93C10Nonlinear control systems
34K40Neutral functional-differential equations
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References:
[1] Bainov, D. D.; Kostadinov, S. I.; Myshkis, A. D.: Asymptotic equivalence of abstract impulsive differential equations. Int. J. Theoret. phys. 35, 383-393 (1996) · Zbl 0843.34051
[2] Benchohra, M.; Górniewicz, L.; Ntouyas, S. K.; Ouahab, A.: Controllability results for impulsive functional differential inclusions. Rep. math. Phys. 54, 211-228 (2004) · Zbl 1130.93310
[3] Benchohra, M.; Ouahab, A.: Controllability results for functional semilinear differential inclusions in Fréchet spaces. Nonlinear analysis 61, 405-423 (2005) · Zbl 1086.34062
[4] Benchohra, M.; Górniewicz, L.; Ntouyas, S. K.; Ouahab, A.: Controllability results for nondensely defined semilinear functional differential equations. Zeitschrift fiir analysis und ihre anwendungen 25, 311-325 (2006) · Zbl 1101.93007
[5] Ballinger, G.; Liu, X.: Boundness for impulsive delay differential equations and applications to population growth models. Nonlinear analysis 53, 1041-1062 (2003) · Zbl 1037.34061
[6] Bashirov, A. E.; Mahmudov, N. I.: On concepts of controllability for deterministic and stochastic systems. Slam journal on control and optimization 37, 1808-1821 (1999) · Zbl 0940.93013
[7] Curtain, R.; Zwart, H. J.: An introduction to infinite dimensional linear systems theory. (1995) · Zbl 0839.93001
[8] Chang, Y. K.: Controllability of impulsive functional differential systems with infinite delay in Banach spaces. Chaos, solitons & fractals 33, 1601-1609 (2007) · Zbl 1136.93006
[9] Duvaut, G.; Lions, J. L.: Inequalities in mechanics and physics. (1976) · Zbl 0331.35002
[10] Dauer, J. P.; Mahmudov, N. I.: Approximate controllability of semilinear functional equations in Hilbert spaces. J. math. Anal applications 273, 310-327 (2002) · Zbl 1017.93019
[11] Do, V. N.: A note on approximate controllability of semilinear systems. Systems and control letters 12, 365-371 (1989) · Zbl 0679.93004
[12] Górniewicz, L.; Ntouyas, S. K.; O’regan, D.: Controllability of semilinear differential equations and inclusions via semigroup theory in Banach spaces. Rep. math. Phys. 56, 437-470 (2005) · Zbl 1185.93016
[13] Gao, C.; Li, K.; Feng, E.; Xiu, Z.: Nonlinear impulsive system of fed-batch culture in fermentative production and its properties. Chaos, solitons & fractals 28, 271-277 (2006) · Zbl 1079.92036
[14] Hino, Y.; Murakami, S.; Naito, T.: Functional differential equations with infinite delay. Lecture notes in mathematics 1473 (1991) · Zbl 0732.34051
[15] M., Jeong J.; H, Roh; H.: Approximate controllability for semilinear retarded systems. J. math. Anal. applications 321, 961-975 (2006) · Zbl 1160.93311
[16] Klamka, J.: Constrained approximate controllability. IEEE transactions on automatic control 45, 1745-1749 (2000) · Zbl 0991.93013
[17] Liu, B.: Controllability of impulsive neutral functional differential inclusions with infinite delay. Nonlinear analysis 60, 1533-1552 (2005) · Zbl 1079.93008
[18] Li, M. L.; Wang, M. S.; Zhang, E. Q.: Controllability of impulsive functional differential systems in Banach spaces. Chaos, solitons & fractals 29, 175-181 (2006) · Zbl 1110.34057
[19] Mahmudov, N. I.: Approximate controllability of semilinear deterministic and stochastic evolution equations in abstract spaces. SIAM journal on control and optimization 42, 1604-1622 (2003) · Zbl 1084.93006
[20] N.I. Mahmudov: Approximate controllability of evolution systems with nonlocal conditions, Nonlinear Analysis, to appear.
[21] Samoilenko, A. M.; Perestyuk, N. A.: Impulsive differential equations. (1995) · Zbl 0837.34003
[22] Tang, S.; Chen, L.: Density-dependent birth rate, birth pulses and their population dynamic consequences. J. math. Biology 44, 185-199 (2002) · Zbl 0990.92033
[23] Wang, L.: Approximate controllability and approximate null controllability of semilinear systems, commun. Pure and applied analysis 5, 953-962 (2006) · Zbl 1127.93310
[24] Yang, T.: Impulsive systems and control. Theory and applications (2001)