Control and Optimization
Zeinab Barary; AllahBakhsh Yazdani Cherati; Somayeh Nemati
Abstract
This paper proposes and analyzes an applicable approach for numerically computing the solution of fractional optimal control-affine problems. The fractional derivative in the problem is considered in the sense of Caputo. The approach is based on a fractional-order hybrid of block-pulse functions and ...
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This paper proposes and analyzes an applicable approach for numerically computing the solution of fractional optimal control-affine problems. The fractional derivative in the problem is considered in the sense of Caputo. The approach is based on a fractional-order hybrid of block-pulse functions and Jacobi polynomials. First, the corresponding Riemann-Liouville fractional integral operator of the introduced basis functions is calculated. Then, an approximation of the fractional derivative of the unknown state function is obtained by considering an approximation in terms of these basis functions. Next, using the dynamical system and applying the fractional integral operator, an approximation of the unknown control function is obtained based on the given approximations of the state function and its derivatives. Subsequently, all the given approximations are substituted into the performance index. Finally, the optimality conditions transform the problem into a system of algebraic equations. An error upper bound of the approximation of a function based on the fractional hybrid functions is provided. The method is applied to several numerical examples, and the experimental results confirm the efficiency and capability of the method. Furthermore, they demonstrate a good agreement between the approximate and exact solutions.
Control and Optimization
Hadi Nasseri; Davood Darvishi Salokolaei; Allahbakhsh Yazdani
Volume 2, Issue 1 , April 2017, , Pages 15-28
Abstract
Linear assignment problem is one of the most important practical models in the literature of linear programming problems. Input data in the cost matrix of the linear assignment problem are not always crisp and sometimes in the practical situations is formulated by the grey systems theory approach. ...
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Linear assignment problem is one of the most important practical models in the literature of linear programming problems. Input data in the cost matrix of the linear assignment problem are not always crisp and sometimes in the practical situations is formulated by the grey systems theory approach. In this way, some researchers have used a whitening technique to solve the grey assignment problem. Since the whitening technique only provides a crisp equivalent model and does not reflect the evolutionary characteristics of a grey set, it cannot keep the uncertainty properties in an interval involving the optimal solution. Based on these shortcomings, in this paper a new direct approach is introduced to solve linear assignment problem in grey environments. For preparing the mentioned method, some theoretical results are given to support the methodology. Finally, a numerical example will be solved to test the validity of the proposed method. Based on the suggested methodology, we emphasize that the same approach can be used whenever any linear programming model is formulated in grey environments.
