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Application of Chebyshev polynomials to the optimal control of time- varying linear systems. (English) Zbl 0555.93024
The operational matrix of backward integration for the shifted Chebyshev polynomials is introduced in this study. The general expression of the shifted Chebyshev polynomial approximation for any two arbitrary functions is also presented. A linear time-varying optimal control system with a quadratic performance measure is solved by using the shifted Chebyshev polynomials. Only a small number of Chebyshev polynomials is needed to produce an excellent result, and the outcome is much better than the solution obtained by using the block-pulse function. So, computer memory capacity and computing time can be saved considerably.

MSC:
93C05 Linear systems in control theory
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
93C99 Model systems in control theory
44A45 Classical operational calculus
93C15 Control/observation systems governed by ordinary differential equations
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