Adaptive control of nonlinearly parameterized systems with a triangular structure. (English) Zbl 1031.93109
By generalizing an earlier result [the author et al., Syst. Control Lett. 37, 267-274 (1999; Zbl 0942.93016)] to all \(n\)th order nonlinear systems with triangular structure and nonlinear parametrization, the authors show that a globally stabilizing and tracking controller guaranteeing a desired precision can be determined. For estimating the unknown parameters, some functions generated by using a min-max optimization problem are introduced in the adaptive controller. Finally, an illustrative example is presented.
Reviewer: Mihail Voicu (Iaşi)
MSC:
| 93C40 | Adaptive control/observation systems |
| 93D21 | Adaptive or robust stabilization |
| 90C47 | Minimax problems in mathematical programming |
Keywords:
Triangular system; nonlinear parametrization; adaptive control; global stability; nonlinear system; adaptive stabilization; tracking controller; min-max optimizationCitations:
Zbl 0942.93016References:
| [1] | Annaswamy, A. M.; Loh, A. P.; Skantze, F. P., Adaptive control of continuous time systems with convex/concave parametrization, Automatica, 34, 33-49 (1998) · Zbl 0910.93049 |
| [2] | Annaswamy, A. M.; Thanomsat, C.; Mehta, N.; Loh, A. P., Applications of adaptive controllers based on nonlinear parametrization, ASME Journal of Dynamic Systems, Measurement, and Control, 120, 477-487 (1998) |
| [3] | Armstrong-Hélouvry, B.; Dupont, P.; Canudas de Wit, C., A survey of models, analysis tools and compensation methods for the control of machines with friction, Automatica, 30, 7, 1083-1138 (1994) · Zbl 0800.93424 |
| [4] | Bosković, J. D., Adaptive control of a class of nonlinearly parametrized plants, IEEE Transactions on Automatic Control, 43, 930-934 (1998) · Zbl 0952.93071 |
| [5] | Fomin, V.; Fradkov, A.; Yakubovich, V., Adaptive control of dynamical systems (1981), Nauka: Nauka Moscow · Zbl 0522.93002 |
| [6] | Hotzel, R., & Karsenti, L. (1997). Tracking control scheme for uncertain systems with nonlinear parametrization. Proceedings of the European control conference; Hotzel, R., & Karsenti, L. (1997). Tracking control scheme for uncertain systems with nonlinear parametrization. Proceedings of the European control conference · Zbl 0957.93074 |
| [7] | Kanellakopoulos, I.; Kokotovic, P. V.; Morse, A. S., Systematic design of adaptive controllers for feedback linearizable systems, IEEE Transactions on Automatic Control, 36, 1241-1253 (1991) · Zbl 0768.93044 |
| [8] | Kojić, A. (2001). Stable identification and control in nonlinear regression problems; Kojić, A. (2001). Stable identification and control in nonlinear regression problems |
| [9] | Kojić, A., & Annaswamy, A. M. (2000). Parameter convergence in systems with convex/concave parameterization. The 2000 American control conference; Kojić, A., & Annaswamy, A. M. (2000). Parameter convergence in systems with convex/concave parameterization. The 2000 American control conference |
| [10] | Kojić, A.; Annaswamy, A. M.; Loh, A.-P.; Lozano, R., Adaptive control of a class of nonlinear systems with convex/concave parameterization, Systems and Control Letters, 37, 267-274 (1999) · Zbl 0942.93016 |
| [11] | Kornenberg, M. J.; Hunter, I. W., The identification of nonlinear biological systems: LNL cascade models, Biological Cybernetics, 55, 125-134 (1986) · Zbl 0611.92001 |
| [12] | Krstić, M.; Kanellakopoulos, I.; Kokotović, P. V., Adaptive nonlinear control without overparameterization, Systems and Control Letters, 19, 177-186 (1992) · Zbl 0763.93043 |
| [13] | Loh, A. P., Annaswamy, A. M., & Skantze, F. P. (1999). Adaptation in the presence of a general nonlinear parametrization: An error model approach. IEEE Transactions on Automatic ControlAC-44; Loh, A. P., Annaswamy, A. M., & Skantze, F. P. (1999). Adaptation in the presence of a general nonlinear parametrization: An error model approach. IEEE Transactions on Automatic ControlAC-44 · Zbl 0958.93051 |
| [14] | Narendra, K. S.; Annaswamy, A. M., Stable adaptive systems (1989), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ · Zbl 0758.93039 |
| [15] | Netto, M. S., Moya, P., Ortega, R., & Annaswamy, A. M. (1999). Adaptive control of a class of first-order nonlinearly parametrized systems. Proceedings of the CDC; Netto, M. S., Moya, P., Ortega, R., & Annaswamy, A. M. (1999). Adaptive control of a class of first-order nonlinearly parametrized systems. Proceedings of the CDC · Zbl 1001.93040 |
| [16] | Ortega, R., Some remarks on adaptive neuro-fuzzy systems, International Journal of Adaptive Control and Signal Processing, 10, 79-83 (1996) · Zbl 0850.93457 |
| [17] | Sastry, S. S.; Bodson, M., Adaptive control: Stability, convergence, and robustness (1989), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ · Zbl 0721.93046 |
| [18] | Seto, D.; Annaswamy, A. M.; Baillieul, J., Adaptive control of nonlinear systems with a triangular structure, IEEE Transactions on Automatic Control, 39, 7, 1411-1428 (1994) · Zbl 0806.93034 |
| [19] | Taylor, D. G.; Kokotovic, P. V.; Marino, R.; Kanellakopoulos, I., Adaptive regulation of nonlinear systems with unmodeled dynamics, IEEE Transactions on Automatic Control, 34, 405-412 (1989) · Zbl 0671.93033 |
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