Browsing by Author "Tehrani, Hojjat Ahsani"

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Citation - WoS: 4
Citation - Scopus: 5
A novel high accurate numerical approach for the time-delay optimal control problems with delay on both state and control variables
(Amer inst Mathematical Sciences-aims, 2022) Hedayati, Mehrnoosh; Baleanu, Dumitru; Tehrani, Hojjat Ahsani; Jahromi, Alireza Fakharzadeh; Skandari, Mohammad Hadi Noori; Baleanu, Dumitru; 56389; Matematik
In this study, we intend to present a numerical method with highly accurate to solve the time-delay optimal control problems with delay on both the state and control variables. These problems can be seen in many sciences such as medicine, biology, chemistry, engineering, etc. Most of the methods used to work out time delay optimal control problems have high complexity and cost of computing. We extend a direct Legendre-Gauss-Lobatto spectral collocation method for numerically solving the issues mentioned above, which have some difficulties with other methods. The simple structure, convergence, and high accuracy of our approach are the advantages that distinguish it from different processes. At first, by replacing the delay functions of state and control variables in the dynamical method, we propose an equivalent system. Then discretizing the problem at the collocation points, we achieve a nonlinear programming problem. We can solve this discrete problem to obtain the approximate solutions for the main problem. Moreover, we prove the gained approximate solutions convergent to the exact optimal solutions when the number of collocation points increases. Finally, we show the capability and the superiority of the presented method by solving some numeral examples and comparing the results with those of others.
Citation - WoS: 3
Citation - Scopus: 3
An Effıcıent Hp Spectral Collocatıon Method For Nonsmooth Optımal Control Problems
(Kybernetika, 2022) Hedayati, Mehrnoosh; Baleanu, Dumitru; Tehrani, Hojjat Ahsani; Jahromi, Alireza Fakharzadeh; Skandari, Mohammad Hadi Noori; Baleanu, Dumitru; 56389; Matematik
One of the most challenging problems in the optimal control theory consists of solving the nonsmooth optimal control problems where several discontinuities may be present in the control variable and derivative of the state variable. Recently some extended spectral collocation methods have been introduced for solving such problems, and a matrix of differentiation is usually used to discretize and to approximate the derivative of the state variable in the particular collocation points. In such methods, there is typically no condition for the continuity of the state variable at the switching points. In this article, we propose an efficient hp spectral collocation method for the general form of nonsmooth optimal control problems based on the operational integration matrix. The time interval of the problem is first partitioned into several variable subintervals, and the problem is then discretized by considering the Legendre-Gauss-Lobatto collocation points. Here, the switching points are unknown parameters, and having solved the final discretized problem, we achieve some approximations for the optimal solutions and the switching points. We solve some comparative numerical test problems to support of the performance of the suggested approach.