Control Lyapunov functions for adaptive nonlinear stabilization. (English) Zbl 0877.93119
Summary: For the problem of stabilization of nonlinear systems linear in unknown constant parameters, we introduce the concept of an adaptive control Lyapunov function (aclf) and use Sontag’s constructive proof of Artstein’s theorem to design an adaptive controller. In this framework the problem of adaptive stabilization of a nonlinear system is reduced to the problem of nonadaptive stabilization of a modified system. To illustrate the construction of aclf’s we give an adaptive backstepping lemma which recovers our earlier design.
Keywords:
Nonlinear control; Adaptive stabilization; Adaptive control Lyapunov functions; BacksteppingReferences:
| [1] | Artstein, Z., Stabilization with relaxed controls, Nonlinear Anal., TMA-7, 1163-1173 (1983) · Zbl 0525.93053 |
| [2] | Jiang, Z. P.; Praly, L., Iterative designs of adaptive controllers for systems with nonlinear integrators, (Proc. 30th IEEE Conf. on Decision and Control. Proc. 30th IEEE Conf. on Decision and Control, Brighton, UK (1991)), 2482-2487 |
| [3] | Kanellakopoulos, I.; Kokotović, P. V.; Marino, R., An extended direct scheme for robust adaptive nonlinear control, Automatica, 27, 247-255 (1991) · Zbl 0729.93046 |
| [4] | Kanellakopoulos, I.; Kokotović, P. V.; Morse, A. S., Systematic design of adaptive controllers for feedback linearizable systems, IEEE Trans. Automat. Control, 36, 1241-1253 (1991) · Zbl 0768.93044 |
| [5] | Krstić, M.; Kanellakopoulos, I.; Kokotović, P. V., Adaptive nonlinear control without overparametrization, Systems Control Lett., 19, 177-185 (1992) · Zbl 0763.93043 |
| [6] | Praly, L.; d’Andréa-Novel, B.; Coron, J.-M., Lyapunov design of stabilizing controllers for cascaded systems, IEEE Trans. Automat. Control, 36, 1177-1181 (1991) |
| [7] | Praly, L.; Bastin, G.; Pomet, J.-B.; Jiang, Z. P., Adaptive stabilization of nonlinear systems, (Kokotović, P. V., Foundations of Adaptive Control (1991), Springer: Springer Berlin), 347-434 · Zbl 0787.93083 |
| [8] | Praly, L., Adaptive regulation: Lyapunov design with a growth condition, Internat. J. Adaptive Control and Signal Processing, 6, 329-351 (1992) · Zbl 0769.93068 |
| [9] | Sontag, E. D., A ‘universal’ construction of Artstein’s theorem on nonlinear stabilization, Systems Control Lett., 13, 117-123 (1989) · Zbl 0684.93063 |
| [10] | Taylor, D.; Kokotović, P. V.; Marino, R.; Kanellakopoulos, I., Adaptive regulation of nonlinear systems with unmodeled dynamics, IEEE Trans. Automat. Control, 34, 405-412 (1989) · Zbl 0671.93033 |
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.
