Approximate controllability of nonlinear deterministic and stochastic systems with unbounded delay. (English) Zbl 1220.93011

Sakthivel, R.; Nieto, Juan J.; Mahmudov, N. I.

Taiwanese J. Math. 14, No. 5, 1777-1797 (2010).

Summary: We consider approximate controllability for nonlinear deterministic and stochastic systems with resolvent operators and unbounded delay. We study the problem of approximate controllability of deterministic nonlinear differential equations with impulsive terms, resolvent operators and unbounded delay. Next, approximate controllability results are being established for a class of nonlinear stochastic differential equations with resolvent operators in a real separable Hilbert space. By using the resolvent operators and fixed point technique, sufficient conditions have been formulated and proved. In this paper, we prove the approximate controllability of nonlinear deterministic and stochastic control systems under the assumption that the corresponding linear system is approximately controllable. Examples are presented to illustrate the utility and applicability of the proposed method.

MSC:

93B05	Controllability
93E03	Stochastic systems in control theory (general)
93E20	Optimal stochastic control

Keywords:

approximate controllability; resolvent operators; impulsive differential equations; neutral equations; stochastic differential equations