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Chebyshev series approach to system identification, analysis and optimal control. (English) Zbl 0538.93013
Various orthogonal functions (e.g. Walsh, block-pulse and Laguerre functions) are now widely used in identification, analysis and design of control systems. In this paper the author makes use of the Chebyshev series for estimation of system’s parameters and initial states as well as for solving the state equations and computing the optimal control in linear-quadratic time-invariant problems. The algorithms derived are similar to those based on other orthogonal functions but have some advantages. This is due to the fact that Chebyshev series permit almost uniform least squares approximation and a more exact representation of multiple integrals.
Reviewer: N.Christov

MSC:
93B30 System identification
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
93B50 Synthesis problems
42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
93B40 Computational methods in systems theory (MSC2010)
93C05 Linear systems in control theory
93C99 Model systems in control theory
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