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Design of an optimal controller for a discrete-time system subject to previewable demand. (English) Zbl 0566.93041

To control in the presence of a finite-horizon previewable demand the state space is extended. The constant discrete-time optimal controller consists of the integral action on the tracking error, the state feedback, and the preview action. In the numerically solved example the order of the extended state is \(n=26\). The quadratic optimization is computed using the O’Donnell-Laub approach, i.e. is based on the eigenstructure of the order 2n matrix associated to the classical symplectic group. The eigenstructure is obtained using the numerically stable properties of the classical orthogonal group.
Reviewer: A.Vaněček

MSC:

93C55 Discrete-time control/observation systems
93B50 Synthesis problems
93C35 Multivariable systems, multidimensional control systems
20G20 Linear algebraic groups over the reals, the complexes, the quaternions
93B35 Sensitivity (robustness)
93C57 Sampled-data control/observation systems
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References:

[1] ATHANS M., Automatica 7 pp 643– (1971) · doi:10.1016/0005-1098(71)90030-6
[2] BRADSHAW A., Int. J. Control 24 pp 275– (1976) · Zbl 0331.93041 · doi:10.1080/00207177608932822
[3] DAVISON E. J., I.E.E.E. Trans, autom. Control 17 pp 621– (1972) · Zbl 0258.49018 · doi:10.1109/TAC.1972.1100084
[4] DAVISON E. J., Automatica 11 pp 461– (1975) · Zbl 0319.93025 · doi:10.1016/0005-1098(75)90022-9
[5] DESOER , C. A. , and WANG , Y. T. , 1980 , inControl and Dynamic Systems,Vol. 16 , edited by C. T. Leondes ( New York Academic Press ), p. 81 .
[6] DOYLE J. C., I.E.E.E. Trans, autom. Control 24 pp 607– (1979) · Zbl 0412.93030 · doi:10.1109/TAC.1979.1102095
[7] FERREIRA P. G., Int. J. Control 23 pp 245– (1976) · Zbl 0329.93020 · doi:10.1080/00207177608922157
[8] FRANCIS B. A., Automatica 12 pp 457– (1976) · Zbl 0344.93028 · doi:10.1016/0005-1098(76)90006-6
[9] FUROTA K., I.E.E.E. Trans, autom. Control 27 pp 788– (1982)
[10] KAILATH T., Linear Systems (1980)
[11] KATAYAMA T., 9th l.F.A.C. World Congress, pp 2– (1984)
[12] KuCERA V., Kybernetika 8 pp 430– (1972)
[13] KWAKERNAAK H., Linear Optimal Control Systems (1972) · Zbl 0276.93001
[14] LAUB A. J., I.E.E.E. Trans, autom. Control 24 pp 913– (1979) · Zbl 0424.65013 · doi:10.1109/TAC.1979.1102178
[15] O’REILLY J., Observers for Linear Systems (1983)
[16] SERAJI H., Int. J. Control 38 pp 843– (1983) · Zbl 0512.93038 · doi:10.1080/00207178308933114
[17] SMITH H. W., Proc. lnstn elect. Engrs 119 pp 1210– (1972) · doi:10.1049/piee.1972.0233
[18] TOMIZUKA M., I.E.E.E. Trans, autom. Control 20 pp 362– (1975) · Zbl 0301.93076 · doi:10.1109/TAC.1975.1100962
[19] TOMIZUKA M., Trans. Am. Soc. mech. Engrs, 101 pp 172– (1979)
[20] YOUNG P. C., Int. J. Control 15 pp 961– (1972) · doi:10.1080/00207177208932211
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