Necessary and sufficient conditions of optimality in the problems of control with fuzzy parameters

Abstract

We study the problem of high-speed operation for linear control systems with fuzzy right-hand sides. For this problem, we introduce the notion of optimal solution and establish necessary and sufficient conditions of optimality in the form of the maximum principle.

Piecewise Constant Controlled Linear Fuzzy Differential Inclusions

“…The applications of fuzzy set theory can be found in many branches of regional, physical, mathematical, differential equations, and engineering sciences. Recently there have been new advances in the theory of fuzzy differential equations [8,10,11,33] and inclusions [1,4,5,7,34] as well as in the theory of controlled fuzzy differential equations [6,19,21,28,27,30] and inclusions [12,13,29,28,32].…”

Averaging of Fuzzy Integrodifferential Inclusions

“…The applications of fuzzy set theory can be found in many branches of science as physical, mathematical, differential equations and engineering sciences. Recently there have been new advances in the theory of fuzzy differential equations [12][13][14][15][16], fuzzy integrodifferential equations [17][18][19][20], differential inclusions with fuzzy right-hand side [21][22][23][24] and fuzzy differential inclusions [25][26][27] as well as in the theory of control fuzzy d i f f e r e n t i a l e q u a t i o n s [ 2 8 -3 0 ] , c o n t r o l f u z z y integrodifferential equations [31][32][33][34][35], controlfuzzy differential inclusions [36][37][38][39], and control fuzzy integrodifferential inclusions [40]. In works [41][42][43][44][45][46][47][48] various schemes of an average for the fuzzy differential equations and inclusions have been considered.…”

Linear Problems of Optimal Control of Fuzzy Maps

“…The applications of fuzzy set theory can be found in many branches of regional, physical, mathematical, differential equations, and engineering sciences. Recently there have been new advances in the theory of fuzzy differential equations [43][44][45][46][47][48][49][50][51][52][53][54][55] and inclusions [50,[56][57][58][59] as well as in the theory of control fuzzy differential equations [60][61][62] and inclusions [63][64][65].…”