Two numerical methods for nonlinear constrained quadratic optimal control problems using linear B-spline functions

Document Type : Research Article


1 Department of Mathematics, Payame Noor University, Tehran, Iran.

2 Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran.


This paper presents two numerical methods for solving the nonlinear constrained optimal control problems including quadratic performance index. The methods are based upon linear B-spline functions. The properties of B-spline functions are presented. Two operational matrices of integration are introduced for related procedures. These matrices are then utilized to reduce the solution of the nonlinear constrained optimal control to a nonlinear programming one to which existing well-developed algorithms may be applied. Illustrative examples are included to demonstrate the validity and applicability of the presented techniques.


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