Abstract
The paper deals with the approximate controllability of a semi-linear stochastic system with multiple delays in control in infinite dimensional spaces. Sufficient conditions for the approximate controllability of the semi-linear control system have been established. The results are obtained using the Banach fixed-point theorem. An example is introduced to show the effectiveness of the result.
Highlights
Controllability is one of the fundamental concepts in mathematical control theory and plays an important role in both deterministic and stochastic control theories
The basic concepts of control theory in finite and infinite dimensional spaces have been introduced in Barnett (1975) and Curtain and Zwart (1995)
Controllability is an important concept pertaining to any control system. It determines whether the state of the system can be steered to a given target state in a prescribed time interval or not
Summary
Controllability is one of the fundamental concepts in mathematical control theory and plays an important role in both deterministic and stochastic control theories. Conceived by Kalman (1963), controllability study was started systematically at the beginning of the 60 s. The basic concepts of control theory in finite and infinite dimensional spaces have been introduced in Barnett (1975) and Curtain and Zwart (1995). The basic theory of semi-groups, on which the solution of an infinite dimensional system is based, has been introduced in Pazy (1983). Dauer and Mahmudov (2002), Balachandran and Dauer (2002) and Triggiani (1975) studied the controllability of deterministic systems in infinite The basic theory of semi-groups, on which the solution of an infinite dimensional system is based, has been introduced in Pazy (1983). Naito (1987) established sufficient conditions for approximate controllability of deterministic semi-linear control system dominated by the linear part using Schauder’s fixed-point theorem. Dauer and Mahmudov (2002), Balachandran and Dauer (2002) and Triggiani (1975) studied the controllability of deterministic systems in infinite
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
