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Optimal control of delay systems via block pulse functions. (English) Zbl 0541.93031
The concept of coefficient shift matrix is introduced to represent delay variables in block pulse series. The optimal control of a linear delay system with quadratic performance index is then studied via block pulse functions, which convert the problem into the minimization of a quadratic form with linear algebraic equation constraints. The solution of the two- point boundary-value problem with both delay and advanced arguments is circumvented. The control variable obtained is piecewise constant.

MSC:
93C05 Linear systems in control theory
34K35 Control problems for functional-differential equations
42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
93C15 Control/observation systems governed by ordinary differential equations
44A45 Classical operational calculus
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