Parametric LQ control. (English) Zbl 0568.93071
The problem considered can be described as follows: For a given linear discrete-time stochastic system determine the linear output feedback from the class of stabilizing feedback gain matrices which minimizes a stationary quadratic criterion. In short, this is what is called a parametric linear quadratic (PLQ) control problem. Some linear and nonlinear descent mapping algorithms for efficiently solving the PLQ problem are introduced and analyzed. Results on their global convergence and their rate of convergence are presented. A numerical example illustrating the PLQ design of low-order controllers for a chemical reactor system is also presented.
Reviewer: P.Stoica
MSC:
| 93E20 | Optimal stochastic control |
| 90C99 | Mathematical programming |
| 93E25 | Computational methods in stochastic control (MSC2010) |
| 93D15 | Stabilization of systems by feedback |
| 93C05 | Linear systems in control theory |
| 93C55 | Discrete-time control/observation systems |
| 93E03 | Stochastic systems in control theory (general) |
Keywords:
linear discrete-time stochastic system; linear output feedback; parametric linear quadratic (PLQ) control problem; descent mapping algorithms; global convergence; rate of convergenceReferences:
| [1] | ACKERMANN J., I.E.E.E. Trans, autom. Control 25 pp 1058– (1980) · Zbl 0483.93041 · doi:10.1109/TAC.1980.1102505 |
| [2] | ANDERSON B. D. O., Linear Optimal Control (1971) · Zbl 0321.49001 |
| [3] | ÅSTRÖM K. J., Introduction to Stochastic Control Theory (1970) |
| [4] | BERGER C. S., I.E.E.E. Trans, autom. Control 19 pp 596– (1974) · doi:10.1109/TAC.1974.1100668 |
| [5] | CHEOK K. C., Proc. 2nd American Control Conf. (1983) |
| [6] | CHOI S. S., I.E.E.E. Trans, autom. Control 19 pp 257– (1974) · Zbl 0278.49039 · doi:10.1109/TAC.1974.1100534 |
| [7] | DAVISON E. J., Automatica 19 pp 169– (1983) · Zbl 0511.93006 · doi:10.1016/0005-1098(83)90089-4 |
| [8] | DORATO P., I.E.E.E. Trans, autom. Control 16 pp 613– (1971) · doi:10.1109/TAC.1971.1099832 |
| [9] | GOLDSTEIN A. A., SIAM J. Control 3 pp 147– (1965) |
| [10] | GOODWIN G. C., I.E.E.E. Trans, autom. Control 24 pp 584– (1979) · Zbl 0412.93047 · doi:10.1109/TAC.1979.1102127 |
| [11] | HALYO N., Proc. Joint Automatica Control Conf (1981) |
| [12] | HORISBERGER H. P., I.E.E.E. Trans, autom. Control 19 pp 434– (1974) · doi:10.1109/TAC.1974.1100585 |
| [13] | JOHANSEN D. E., Advances in Control Systems 4 (1966) |
| [14] | KURTARAN B., Int. J. Control 19 pp 797– (1974) · Zbl 0277.93016 · doi:10.1080/00207177408932674 |
| [15] | LEVINE W. S., I.E.E.E. Trans, autom. Control 15 pp 44– (1970) · doi:10.1109/TAC.1970.1099363 |
| [16] | MÄKILÄ , P. M. , 1982 , Ph.D. thesis , Åbo Akademi , Åbo , Finland ; 1983, Proc. 2nd AmericanControl Conf., San Francisco; 1984, Automatica, 20, 671 . |
| [17] | MÄKILÄ P. M., Automatica 20 pp 15– (1984) · Zbl 0535.93068 · doi:10.1016/0005-1098(84)90061-X |
| [18] | MILLER L. F., Int. J. Control 27 pp 455– (1978) · Zbl 0373.93016 · doi:10.1080/00207177808922383 |
| [19] | O’REILLY J., Int. J. Systems Sci. 9 pp 9– (1978) · Zbl 0371.93005 · doi:10.1080/00207727808941674 |
| [20] | SANDELL N. R., I.E.E.E. Trans, autom.Control 23 pp 108– (1978) · Zbl 0385.93001 · doi:10.1109/TAC.1978.1101704 |
| [21] | SILVA , J. M. , 1978 , Ph.D. thesis , University of California , Berkeley . |
| [22] | SÖDERSTRÖM T., I.E.E.E. Trans, autom. Control 23 pp 1100– · Zbl 0388.93019 · doi:10.1109/TAC.1978.1101917 |
| [23] | SRINIVASA Y. G., Proc. 18th I.E.E.E. Conf. on Decision and Control (1979) |
| [24] | WENK C. J., I.E.E.E. Trans, autom. Control 25 pp 496– (1980) · Zbl 0431.49001 · doi:10.1109/TAC.1980.1102373 |
| [25] | WESTERLUND T., I.E.E.E. Trans, autom. Control 26 pp 885– (1981) · doi:10.1109/TAC.1981.1102738 |
| [26] | YAHAGI T., Int. J. Control 18 pp 849– (1973) · Zbl 0273.49043 · doi:10.1080/00207177308932562 |
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
