Kybernetika 51 no. 1, 81-98, 2015

Direct solution of nonlinear constrained quadratic optimal control problems using B-spline functions

Yousef Edrisi Tabriz and Mehrdad LakestaniDOI: 10.14736/kyb-2015-1-0081

Abstract:

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.

Keywords:

optimal control problem, B-spline functions, derivative matrix, collocation method

Classification:

49N10, 65D07, 65R10, 65L60

paper.pdf

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