Analysis, parameter estimation and optimal control of time-delay systems via Chebyshev series. (English) Zbl 0562.93034
Summary: The Chebyshev delay operational matrix is introduced first and then applied to approximate the solutions of linear time-invariant and time- varying delay systems with arbitrary time delay. The parameter identification problem of the delay control system is also studied. Furthermore, an approximate solution of the optimal control problem with quadratic performance measure is then discussed. Four examples are given, and the results are shown to be very accurate and satisfactory.
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.) |
| 44A45 | Classical operational calculus |
| 93B30 | System identification |
| 93C99 | Model systems in control theory |
Keywords:
Chebyshev delay operational matrix; arbitrary time delay; parameter identification; approximate solution; quadratic performanceReferences:
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