×

zbMATH — the first resource for mathematics

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
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] ABRAMOWITZ M., Handbook of Mathematical Functions (1967)
[2] BARNETT S., Matrix Method for Engineers and Scientists (1979) · Zbl 0507.15001
[3] CHEN W. L., I.E.E.E. Trans, autom. Control 23 pp 1023– (1978) · Zbl 0388.93029 · doi:10.1109/TAC.1978.1101888
[4] CHOU J. H., Int. J. Control 41 pp 135– (1985) · Zbl 0555.93024 · doi:10.1080/0020718508961115
[5] HALE J. K., Functional Differential Equations (1971) · Zbl 0222.34003 · doi:10.1007/978-1-4615-9968-5
[6] HORNG I. R., Int. J. Control 41 pp 549– (1985) · Zbl 0555.93017 · doi:10.1080/0020718508961146
[7] HSIA T. C., System Identification (1979)
[8] HWANG G., J. Optim. Theory Applic (1984)
[9] KUNG F. C., A.S.M.E. Trans. J. Dynam. Syst. Meas. Control 105 pp 297– (1983) · Zbl 0525.93036 · doi:10.1115/1.3140675
[10] PARASKEVOPOULOS P. N., J. Franklin Inst. 316 pp 135– (1983) · Zbl 0538.93013 · doi:10.1016/0016-0032(83)90082-0
[11] RAO G. P., Int. J. Systems Sci. 15 pp 9– (1984) · Zbl 0539.93044 · doi:10.1080/00207728408926541
[12] SHIH Y. P., A.S.M.E. Trans. J. Dynam. Syst. Meas. Control 102 pp 159– (1980) · Zbl 0446.93051 · doi:10.1115/1.3139626
[13] TAKAHASHI Y., Control and Dynamic Systems (1970)
[14] Tsoi A. C., Int. J. Control 21 pp 39– (1975) · Zbl 0314.34073 · doi:10.1080/00207177508921968
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.