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Analysis and optimal control of time-varying linear systems via shifted Legendre polynomials. (English) Zbl 0562.93035
Summary: This paper extends the application of shifted Legendre polynomial expansion to time-varying systems. The extension is achieved through representing the product of two shifted Legendre series in a new shifted Legendre series. With this treatment of the product of two time functions, the operational properties of the shifted Legendre polynomials are fully applied to the analysis and optimal control of time-varying linear systems with quadratic performance index.

MSC:
93C05 Linear systems in control theory
42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
93C99 Model systems in control theory
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
44A45 Classical operational calculus
34K35 Control problems for functional-differential equations
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