Average \(\mathcal H_2\) control by randomized algorithms. (English) Zbl 1019.93017
For finding an average \(H_2\) control for robust stabilization, a mean quadratic performance criterion is minimized. Approximate optimal solutions of this mean value function minimization problem are obtained by approximating the mean by its empirical mean. The method is applied then to an active suspension system.
Reviewer: Kurt Marti (Neubiberg/München)
Keywords:
approximate optimal solutions; average \(H_2\) control; robust stabilization; function minimization; empirical mean; active suspension systemReferences:
| [1] | BOERS, Y., WEILAND, S. and DAMEN, A. A. H. Expected H2 performance control for systems with statistical uncertainty. Preprints of the 2nd IFAC Symposium on Robust Control Design. pp.387–392. Budapest, Hungary |
| [2] | BOERS, Y., WEILAND, S. and DAMEN, A. A. H. Average H2 performance design by randomized algorithms. Proceedings of the 37st IEEE Conference on Decision and Control. Tampa, FL, USA. · Zbl 1019.93017 |
| [3] | BOERS, Y., WEILAND, S. and DAMEN, A. A. H. Constant feedback HI control of systems with statistical uncertainty. Proceedings of the 37st IEEE Conference on Decision and Control. Tampa, FL, USA. · Zbl 1019.93017 |
| [4] | DORATO P., Linear-Quadratic Control (1995) · Zbl 0838.93004 |
| [5] | HAGWOOD, N. W. 1991. ”Cost averaging techniques for robust control of parametrically uncertain systems”. MIT. PhD thesis |
| [6] | DOI: 10.1109/9.250566 · Zbl 0792.93052 · doi:10.1109/9.250566 |
| [7] | DOI: 10.1109/TAC.1986.1104098 · Zbl 0579.93028 · doi:10.1109/TAC.1986.1104098 |
| [8] | HUISMAN, R. 1994. ”A controller and observer for active suspensions with preview”. Einhoven University of Technology. PhD thesis |
| [9] | KHARGONEKAR, P. and TIKKU, A. Randomized algorithms for robust control analysis and synthesis have polynomial complexity. Proceedings of the 35th Conference on Decision and Control. pp.3470–3475. Kobe, Japan |
| [10] | DOI: 10.1002/rnc.4590050104 · Zbl 0825.93972 · doi:10.1002/rnc.4590050104 |
| [11] | DOI: 10.1109/9.587338 · Zbl 0886.93074 · doi:10.1109/9.587338 |
| [12] | POLDERMAN J. W., Introduction to Mathematical Systems Theory (1998) · doi:10.1007/978-1-4757-2953-5 |
| [13] | DOI: 10.1109/9.250479 · Zbl 0774.93065 · doi:10.1109/9.250479 |
| [14] | RAY L. R., IEEE Transactions on Automatic Control 36 pp 82– (1993) |
| [15] | DOI: 10.1016/0005-1098(93)90187-X · Zbl 0800.93302 · doi:10.1016/0005-1098(93)90187-X |
| [16] | SABERI A., H2 Optimal Control (1995) |
| [17] | TEMPO, R., BAI, E. W. and DABBENE, F. Probabilistic robustness analysis: Explicit bounds for the number of samples. Proceedings of the 35th Conference on Decision and Control. pp.3424–3428. Kobe, Japan · Zbl 0901.93017 |
| [18] | VIDYASAGAR, M. Statistical learning theory and its applications to randomized algorithms for robust controller synthesis. Plenary Lectures and Mini-Coarse s at the European Control Conference. pp.161–189. Brussels, Belgium |
| [19] | VIDYASAGAR M., A Learning and Generalization (1971) |
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.
