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Legendre wavelets method for constrained optimal control problems. (English) Zbl 1001.49033
Summary: A numerical method for solving nonlinear optimal control problems with inequality constraints is presented in this paper. The method is based upon Legendre wavelet approximations. The properties of Legendre wavelets are first presented. The operational matrix of integration and the Gauss method are then utilized to reduce the optimal control problem to the solution of algebraic equations. The inequality constraints are converted to a system of algebraic equalities; these equalities are then collocated at the Gauss nodes. Illustrative examples are included to demonstrate the validity and applicability of the technique.

MSC:
49M30 Other numerical methods in calculus of variations (MSC2010)
49J15 Existence theories for optimal control problems involving ordinary differential equations
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
65T60 Numerical methods for wavelets
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