جستجوی مقالات مرتبط با کلیدواژه « ‎Optimal control » در نشریات گروه « ریاضی »

Functional analysis was an  important development in the viewpoint of mathematicians in examining the behavior of functions as a set (space of functions). The important concept of single space and the distance of its points, invented by ‎Fréchet‎ in the early 20th century, and the fusion of algebraic and topological concepts eventually led to the establishment of this branch of mathematics around 1933. The first Iranian mathematician to make a mark in this field was Heydar Radjavi, who contributed to the field in Iran from 1963 to 1968. Another branch of this field is called nonlinear functional analysis, and Behzad Djafari-Rouhani was the first specialist in this branch who worked in the country from 19‎87‎ onwards. Another key figure in the development and expansion of this branch in the country is Jafar Zafarani. This article, after outlining the history of functional analysis, will provide a brief overview of his contributions to this field. Through a conversation with him, we will delve into his experiences and insights from various aspects of his professional life.

Using mathematical models to describe infectious diseases and then how to control and eliminate them by vaccines or other treatments, is a great help to public health organizations. Eradication of this category of diseases is possible when treatments are prescribed at the right time and with the right amount and process; In this regard, optimal control theory has been applied as a successful tool. The main purpose of this article is to review the existing literature considering such strategies in dealing with infectious diseases in the form of the famous basic model SIR. For this purpose, this study, deals with the way to use the control functions and how to explain the provided solutions, indeed the aims are to investigate susceptible, infected, and recovered populations in terms of the required goals, among the performed activities by evaluation and analyzing. Based on the number of used control variables in the treatment model, which indicate different methods of simultaneous prevention, including vaccination, treatment of infection, quarantine, and like or, the type of model, this study has been categorized and the results are presented. Also, in this review, the methods of implementing models from a numerical computation point of view and reality have also been discussed and time delay, stochastic, and discrete-time models in the case of SIR are also investigated. This review would help the researchers in order to have knowledge about the subject and activities carried out to continue research in this area are very helpful.

This article introduces an iterative method for solving discrete optimal control problems involving interconnected nonlinear systems. Using this approach, the discrete and coupled nonlinear boundary value problem (BVP) obtained from the necessary optimality conditions transforms into a sequence of linear time invariant BVPs. Furthermore, the linear BVP at each iteration of the proposed method consists of several decoupled sub-problems, which can be solved in parallel and are unrelated to each other. The solution of these problems, employing common techniques for solving linear difference equations, leads to an optimal control law in a converging series form with uniform convergence. Moreover, a practical approach is presented to extend the designed optimal control to a feedback form. Subsequently, the implementation of the proposed method involves the design of a highly accurate iterative algorithm with low computational complexity, ensuring that the suboptimal control law is obtained with a minimal number of iterations. Finally, the efficacy of this technique is demonstrated through simulation and the solution of various numerical examples.

In this paper, the optimal control of delay systems with piecewise constant delay function is investigated. Using Chebyshev hybrid functions, an approximate method is proposed to obtain the optimal solution to the control problem of linear delay systems. In order to present an approximate method, integral, product of multiplication and delay operational matrices of the hybrid functions have been introduced and used to solve the problem. The optimal control problem is transformed into an optimization problem with the help of the operational matrices and then solving it, an approximate solution to the original problem is obtained. Efficiency and accuracy of the proposed method are illustrated with two examples of the optimal control problem. ‎‎