zbMATH — the first resource for mathematics

Adaptive stabilization using a variable sampling rate. (English) Zbl 0845.93074
Consider an adaptive stabilization problem for a single-input single-output linear minimum phase system (1) \(\begin{cases} \dot x = Ax + Bu \\ y = Cx. \end{cases}\) such that \(CB > 0\), by means of the feedback law (2) \(u = - ky\), \(\dot k = y^2\). It is known that, when the feedback is implemented digitally, for particular choices of the initial values \(x_0\), \(k_0\) and of the (constant) sampling rate \(h\), the computed solution may diverge, in contrast with the prediction of the continuous time theoretical results. To face this problem the author considers variable sampling rates and a discrete analog of (2). The control gain depends on the current sampling rate at each step. Stabilization is achieved in such a way that the sequence of measured outputs tends to zero. Results are provided for both cases where the sign of CB is known or not known.

93D21 Adaptive or robust stabilization
93C57 Sampled-data control/observation systems
Full Text: DOI
[1] DOI: 10.1137/0305011 · Zbl 0158.03701 · doi:10.1137/0305011
[2] BYRNES , C. I. , WILLEMS J. C. , 1984a , Global adaptive stabilization in the absence of information on the sign of the high frequency gain . Proceedings of the INRIA Conference on Analysis and Optimization of Systems ( Springer-Verlag ), pp. 49 – 57 ; 1984 b, Adaptive stabilization of multivariable linear systems.Proceedings of the IEEE 23rd Conference on Decision and Control, Las Vegas, California, U.S.A., pp. 1574–1577 .
[3] ILCHMANN A., Non-identifier-based High-gain Adaptive Control (1993) · Zbl 0786.93059
[4] DOI: 10.1016/0167-6911(87)90077-6 · Zbl 0632.93046 · doi:10.1016/0167-6911(87)90077-6
[5] LEE T. H., IEEE Transactions on Automatic Control 31 pp 477–
[6] MARTENSSEN , B. , 1986 , Adaptive stabilization. Doctoral Dissertation, Department of Automatic Control , Lund University , Sweden , LUTFD2/(TFRT 1028)/l–122/ lpar;1986) .
[7] OWENS D. H., Feedback and Multivariable Systems (1978) · Zbl 0446.93001
[8] DOI: 10.1093/imamci/4.2.167 · Zbl 0631.93058 · doi:10.1093/imamci/4.2.167
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.