Abstract
We consider the robust tracking problem for a discrete time control object with unknown upper bounds on the perturbations. The transition function in the nominal model of the controllable object is assumed to be known, while upper bounds on the external perturbation, measurement noise, and operator perturbations with respect to both output and control are assumed to be unknown or rough. Current estimates of upper bounds on the perturbations are obtained from measurement data with the quality criterion of the tracking problem as the identification criterion.
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References
The Modeling of Uncertainty in Control Systems, in Lecture Notes in Control and Information Sciences, Smith, R.S. and Dahleh, M., Eds., London: Springer-Verlag, 1994, vol. 192.
Special Issue on System Identification, IEEE Trans. Autom. Control, Ljung, L. and Vicino, A., Eds., 2005, vol. 50, no. 10, pp. 1473–1634.
Data-Based Modelling and System Identification (Special Issue), Automatica, Soderstrom, T., van den Hof, P., Wahlberg, B., and Weiland, S., Eds., 2005, vol. 41, no. 3, pp. 357–562.
Gevers, M., A Personal View of the Development of System Identification, IEEE Control Syst. Mag., 2006, vol. 26, no. 6, pp. 93–105.
Hjalmarsson, H., From Experiment Design to Closed-Loop Control, Automatica, 2005, vol. 41, pp. 393–438.
Polyak, B.T. and Shcherbakov, P.S., Robastnaya ustoichivost’ i upravlenie (Robust Stability and Control), Moscow: Nauka, 2002.
Zhou, K., Doyle, J.C., and Glover, K., Robust and Optimal Control, Upper Saddle River: Prentice Hall, 1996.
Khammash, M. and Pearson, J.B., Analysis and Design for Robust Performance with Structured Uncertainty, Syst. Control Lett., 1993, vol. 20, pp. 179–187.
Khammash, M. and Pearson, J.B., Performance Robustness of Discrete-Time Systems with Structured Uncertainty, IEEE Trans. Autom. Control, 1991, vol. 36, no. 4, pp. 398–412.
Sokolov, V.F., Robust Control in ℓ 1-Formulation: Model Validation and Perturbation Weight Estimation, Autom. Remote Control, 2003, vol. 64, no. 11, pp. 1769–1782.
Sokolov, V.F., Control-Oriented Model Validation and Errors Quantification in the ℓ 1 Setup, IEEE Trans. Autom. Control, 2005, vol. 50, no. 10, pp. 1501–1509.
Mäkilä, P.M., Partington, J.R., and Gustafsson, T.K., Worst-case Control-relevant Identification, Automatica, 1995, vol. 31, no. 12, pp. 1799–1819.
Dahleh, M.A. and Doyle, J.C., From Data to Control, in Lecture Notes in Control and Inform. Sci., The Modeling of Uncertainty in Control Systems, 1994, Lodon: Springer-Verlag, vol. 192, pp. 61–63.
Sokolov, V.F., Asymptotically Suboptimal Robust Control for a Discrete Object with Unknown Perturbations Weights, Dokl. Ross. Akad. Nauk, 2010, vol. 431, no. 1, pp. 32–35.
Sokolov, V.F., Suboptimal Robust Synthesis for MIMO Plant under Coprime Factor Perturbations, Syst. Control Lett., vol. 57(4), 2008, pp. 348–355.
Sokolov, V.F., Asymptotic Robust Performance of the Discrete Tracking System in the ℓ 1-Metric, Autom. Remote Control, 1999, vol. 60, no. 1, part 2, pp. 82–92.
Sokolov, V.F., Estimating Performance of the Robust Control System under Unknown Upper Perturbation Boundaries and Measurement Noise, Autom. Remote Control, 2010, vol. 71, no. 9, pp. 1741–1757.
Fomin, V.N., Fradkov, A.L., and Yakubovich, V.A., Adaptivnoe upravlenie dinamicheskimi ob”ektami (Adaptive Control for Dynamic Objects), Moscow: Nauka, 1981.
Sokolov, V.F., Design of Suboptimal Robust Controllers under Unknown Weights of Perturbations, Autom. Remote Control, 2007, vol. 68, no. 3, pp. 487–502.
Sokolov, V.F., ℓ 1-Suboptimal Robust Controller Design for Discrete Linear SISO Plants with Structured Uncertainty, Autom. Remote Control, 1999, vol. 60, no. 11, part 1, pp. 1587–1601.
Sokolov, V.F., ℓ 1 Optimal Robust Controller for SISO Plant under Coprime Factor Disturbances, IEEE Trans. Automat. Control, 2000, vol. 45, pp. 2339–2345.
Khammash, M.H., A New Approach to the Solution of the ℓ 1 Control Problem: The Scaled-Q Method, IEEE Trans. Autom. Control, 2000, vol. 45, pp. 180–187.
Gavurin, M.K. and Malozemov, V.N., Ekstremal’nye zadachi s lineinymi ogranicheniyami (Extremal Problems with Linear Constraints), Leningrad: Leningr. Gos. Univ., 1984.
Sokolov, V.F., Adaptive Suboptimal Control of a Linear System with Bounded Disturbances, Syst. Control Lett., 1985, vol. 6, pp. 93–98.
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Original Russian Text © V.F. Sokolov, 2013, published in Avtomatika i Telemekhanika, 2013, No. 1, pp. 98–115.
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Sokolov, V.F. Robust tracking with unknown upper bounds on the perturbations and measurement noise. Autom Remote Control 74, 76–89 (2013). https://doi.org/10.1134/S0005117913010074
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DOI: https://doi.org/10.1134/S0005117913010074