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Linear quadratic optimal control problems with inequality constraints via rationalized Haar functions. (English) Zbl 1081.49026
Summary: A numerical method for solving linear-quadratic optimal control problems with inequality constraints is presented in this paper. The method is based upon rationalized Haar functions approximations. The properties of rationalized Haar functions are first presented. The operational matrix of integration is then utilized to reduce the optimal control problems to the solution of algebraic equations. The inequality constrains are converted to a system of algebraic equalities and these equalities are then collocated at Netwon-Cotes nodes. Illustrative examples are included to demonstrate the validity and applicability of the technique.

49N10 Linear-quadratic optimal control problems
49K30 Optimality conditions for solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.)
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)