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Báo cáo nghiên cứu khoa học: "sự tồn tại của giải phương trình vi phân điều khiển mờ"

Gần đây, lĩnh vực phương trình vi phân đã được nghiên cứu trong một phương pháp rất trừu tượng. Thay vì xem xét hành vi của một trong những giải pháp của một phương trình vi phân, một trong những nghiên cứu bó giải pháp của nó (xem [10-11]). Thay vì nghiên cứu một phương trình vi phân, một nghiên cứu khác biệt bao gồm (xem [9]). | TẠP CHÍ PHÁT TRIỂN KH CN TẬP 10 SÓ 05 - 2007 EXISTENCE OF SOLUTIONS OF FUZZY CONTROL DIFFERENTIAL EQUATIONS Nguyen Dinh Phu and Tran Thanh Tung University of Natural Science VNU-HCM Manuscript received on May 25th 2006 Manuscript received on May 71th 2007 ABSTRACT Recently the field of differential equations has been studying in a very abstract method. Instead of considering the behaviour of one solution of a differential equation one studies its sheaf-solution see 10-11 . Instead of studying a differential equation one studies differential inclusion see 9 . Especially one studies fuzzy differential equation a differential equation whose variables and derivative are fuzzy sets see 1-7 .In this paper a fuzzy differential equation is generalized to be fuzzy control differential equation FCDE and we present the existence and comparison of solutions of FCDE . This paper is a continuation of our works in this direction see 10-13 . Keywords Fuzzy theory Differential equations Control theory Fuzzy differential equations 1. INTRODUCTION In 1-7 the authors considered fuzzy differential equations FDE and had some important results on existence and comparison of solutions of FDE DjjX t f t x t 1.1 where x t0 x0 e H0 c En x t e En t e t0 T I c R and f I X En En. In this paper we consider a fuzzy control differential equation FCDE as following Dhx t f t x t u t 1.2 where x t0 x0 e H0 c En x t e En u t e Ep t e t0 T J I c R and f I X En X Ep En and study existence of solutions of FCDE. The paper is organized as follows in section 2 we recall some basic concepts and notations which are useful in next sections. In sections 3 and 4 we present the existence of solutions and compare two solutions of FCDE. 2. PRELIMINARIES We recall some notations and concepts presented in detail in recent series works of Lakshmikantham V. et al. See 4-7 . Let KC Rn denote the collection of all nonempty compact and convex subsets of Rn. Given A B in KC Rn the Hausdorff distance between A and B defined