Abstract
In this paper, we study the e-approximate controllability for the semilinear fuzzy integrodifferential control system in fuzzy vector space. This is an extension of result of Kwun et al.[4] to n-dimensional fuzzy vector space.
Highlights
Many authors have studied several concepts of fuzzy systems
Kwun and Park 2 proved the existence of fuzzy optimal control for the nonlinear fuzzy differential system with nonlocal initial condition in EN1 by using Kuhn-Tucker theorems
Fuzzy integrodifferential equations are a field of interest, due to their applicability to the analysis of phenomena with memory where imprecision is inherent
Summary
Many authors have studied several concepts of fuzzy systems. Diamond and Kloeden 1 proved the fuzzy optimal control for the following system: xtatxtut , x 0 x0, 1.1 where x · and u · are nonempty compact interval-valued functions on E1. Balasubramaniam and Muralisankar 3 proved the existence and uniqueness of fuzzy solutions for the semilinear fuzzy integrodifferential equation with nonlocal initial condition. They considered the semilinear one-dimensional heat equation on a connected domain 0, 1 for material with. In one-dimensional fuzzy vector space EN1 , Park et al 4 proved the existence and uniqueness of fuzzy solutions and presented the sufficient condition of nonlocal controllability for the following semilinear fuzzy integrodifferential equation with nonlocal initial condition: dx t dt. We study the the existence and uniqueness of solutions and controllability for the following semilinear fuzzy integrodifferential equations: dxi t dt. G t − s xi s ds fi t, xi t ui t on ENi , 1.3 xi 0 gi xi x0i ∈ ENi i 1, 2, . . . , n , where Ai : 0, T → ENi is fuzzy coefficient, ENi is the set of all upper semicontinuously convex fuzzy numbers on R with ENi / ENj i / j , fi : 0, T × ENi → ENi is a nonlinear regular fuzzy function, gi : ENi → ENi is a nonlinear continuous function, G t is n × n continuous matrix such that dG t xi/dt is continuous for xi ∈ ENi and t ∈ 0, T with G t ≤ k, k > 0, ui : 0, T → ENi is control function and x0i ∈ ENi is initial value
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
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
