Geodesic
Direct solution of nonlinear constrained quadratic optimal control problems using B-spline functions
Kybernetika, Tome 51 (2015) no. 1, pp. 81-98.

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In this paper, a new numerical method for solving the nonlinear constrained optimal control with quadratic performance index is presented. The method is based upon B-spline functions. The properties of B-spline functions are presented. The operational matrix of derivative ($\mathbf{D}_\phi$) and integration matrix ($\mathbf{P}$) are introduced. These matrices are utilized to reduce the solution of nonlinear constrained quadratic optimal control to the solution of nonlinear programming one to which existing well-developed algorithms may be applied. Illustrative examples are included to demonstrate the validity and applicability of the technique.
DOI : 10.14736/kyb-2015-1-0081
Classification : 49M25, 49N10, 65D07, 65L60, 65R10
Keywords: optimal control problem; B-spline functions; derivative matrix; collocation method 
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Edrisi Tabriz, Yousef; Lakestani, Mehrdad. Direct solution of nonlinear constrained quadratic optimal control problems using B-spline functions. Kybernetika, Tome 51 (2015) no. 1, pp. 81-98. doi : 10.14736/kyb-2015-1-0081. http://geodesic.mathdoc.fr/articles/10.14736/kyb-2015-1-0081/

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