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Direct solution of nonlinear constrained quadratic optimal control problems using B-spline functions. (English) Zbl 1340.49034
Summary: 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.

MSC:
49N10 Linear-quadratic optimal control problems
65D07 Numerical computation using splines
65R10 Numerical methods for integral transforms
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
Software:
Maple; NLPQL
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