Nonlinear Fuzzy Differential Equation with Time Delay and Optimal Control Problem

Witayakiattilerd, Wichai

doi:10.1155/2015/659072

Cited by 7 publications

(1 citation statement)

References 15 publications

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“…Additionally, in [16] , fuzzy optimal control for a class of fuzzy dynamical with fuzzy coefficients and certain boundary conditions has been studied. Moreover, the existence of a solution to optimal control problem of a non-linear fuzzy dynamical system constrained by initial value has been presented in [17] . Additionally, in [18] , the Pontryagin maximum principle has been used to obtain a necessary optimality condition based on which the fuzzy optimal control function for a class of linear fuzzy dynamical systems is obtained.…”

Section: Introductionmentioning

confidence: 99%

Tracking Control of a Class of Fuzzy Dynamical Systems under the Concept of Granular Differentiability

Abbasi¹,

Jalali²

2023

Fuzzy Information and Engineering

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In this work, the tracking control of a class of uncertain linear dynamical systems is investigated. The uncertainty is considered to be represented as fuzzy numbers, and hence, these uncertain dynamical systems are referred to as fuzzy linear dynamical systems, which are presented in the form of fuzzy differential equations (FDEs). The solution of an FDE is found using an approach called relative-distance-measure fuzzy interval arithmetic and under the granular differentiability concept. The control objective is to provide a control law such that the output of the system tracks a desired reference input in the presence of uncertainties. To this end, a theorem is proposed, which suggests that the control law should take the form of a feedback of fuzzy states with fuzzy gains and a fuzzy pre-compensator. However, since the fuzzy states of the system may not always be measurable, a fuzzy observer is designed for the estimation of such fuzzy states. It is also clearly shown that the generalized Hukuhara differentiability concept is unable for solving the problem examined in this study. Finally, the efficiency of the approach is examined for a plane landing control problem.

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Section: Introductionmentioning

confidence: 99%

Tracking Control of a Class of Fuzzy Dynamical Systems under the Concept of Granular Differentiability

Abbasi¹,

Jalali²

2023

Fuzzy Information and Engineering

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Optimal Control Problems for a Semilinear Evolution System with Infinite Delay

Mokkedem

2017

Appl Math Optim

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Fuzzy Phase Trajectories in Hemispherical Resonator Gyroscopes

2021

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The paper considers elementary fuzzy oscillator models represented by hard and fuzzy second-order differential equations with hard and fuzzy initial conditions. Linear models describe wave processes in ring resonators of hemispherical resonator gyroscopes.We show that in the case 1 (a hard model with fuzzy initial conditions), when there is no internal friction (model 1), phase trajectories appear as a fuzzy centre shaped as an elliptical ring. When internal friction is present (model 2), phase trajectories appear as a fuzzy focus shaped as a circular logarithmic spiral. In the case 2, for a fuzzy hemispherical resonator gyroscope model with hard initial conditions, when there is no internal friction (model 1), a representative point of a fuzzy phase trajectory does not stop or increase its oscillations with time, meaning that the system is asymptotically unstable, while for the model 2 the origin singularity is a fuzzy stable focus. In the case 3, for a fuzzy hemispherical resonator gyroscope model with fuzzy initial conditions, when there is no internal friction (model 1), there is a fuzzy asymptotic instability in the model 1 of a hemispherical resonator gyroscope, while in the presence of internal friction (model 2), the phase trajectory is also a function of time and controls the asymptotic stability of the fuzzy model 2 of a hemispherical resonator gyroscope. Asymptotic stability is determined for all cases and models

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Nonlinear Fuzzy Differential Equation with Time Delay and Optimal Control Problem

Cited by 7 publications

References 15 publications

Tracking Control of a Class of Fuzzy Dynamical Systems under the Concept of Granular Differentiability

Tracking Control of a Class of Fuzzy Dynamical Systems under the Concept of Granular Differentiability

Optimal Control Problems for a Semilinear Evolution System with Infinite Delay

Fuzzy Phase Trajectories in Hemispherical Resonator Gyroscopes

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