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Solution of linear two-point boundary value problems and optimal control of time-varying systems by shifted Chebyshev approximations. (English) Zbl 0714.49032

Summary: A method for finding the solution of a linear two-point boundary value problem with time-varying coefficients is discussed. Properties of shifted Chebyshev series are first briefly presented and the transformation matrix relating the back vector to the current time vector together with the operational matrix are utilized to solve the two-point boundary value problems. This approach can be applied to obtain the optimal control of linear time-varying systems subject to quadratic cost criteria. An illustrative example is given.

MSC:

49M15 Newton-type methods
49N05 Linear optimal control problems
65L10 Numerical solution of boundary value problems involving ordinary differential equations
42C05 Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis
49J15 Existence theories for optimal control problems involving ordinary differential equations
65K10 Numerical optimization and variational techniques
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