Shahid Chamran University of AhvazJournal of Advanced Mathematical Modeling2251-808812220220622Optimal control of linear delay systems involving piecewise constant delay function using hybrid Chebyshev-block pulse methodOptimal control of linear delay systems involving piecewise constant delay function using hybrid Chebyshev-block pulse method1852001758810.22055/jamm.2022.39845.2005FASayyed Mohammad HoseiniDepartment of Mathematics, Faculty of Basic Sciences, Ayatollah Boroujerdi University, Boroujerd, Iran0000-0003-0551-437XJournal Article20220124In 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. 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. https://jamm.scu.ac.ir/article_17588_07b5d5b1de64c2335f96b8f897b42089.pdf