ISSN 0021-3454 (print version)
ISSN 2500-0381 (online version)
Menu

7
Issue
vol 63 / July, 2020
Article

DOI 10.17586/0021-3454-2018-61-4-304-308

UDC 681.51

MODIFIED METHOD FOR PARAMETERS ESTIMATING IN FINITE-TIME CONTROL SYNTHESIS

K. A. Zimenko
ITMO University, Saint Petersburg, 197101, Russian Federation; Senior Scientific Researcher


A. E. Polyakov
Institut national de rechercheeninformatique et enautomatique, Lille, 59650, France ; Senior Researcher


D. V. Efimov
INRIA (Institut national de recherche en informatique et en automatique), Lille, 59650, France; Principal investigator of the first rank


A. S. Kremlev
ITMO University, Saint Petersburg, 197101, Russian Federation; Associate professor


Read the full article 

Abstract. A modified method for estimating parameters used in finite-time control synthesis is proposed. The object under the control is a chain of consecutively connected integrators in the presence of external disturbances and parametric uncertainties. It is assumed that the state vector is available for measurement. Results presented in the previous papers of the authors are extended. The developed method does not require the execution of additional computational procedures, such as the search for parameters on a certain numerical grid and allows to obtain the estimates of the necessary parameters analytically. Thus, the presented method is reported to simplify considerably the synthesis of a finite-time regulator.
Keywords: control parameters estimation, finite-time stability, state feedback control

References:
  1. Orlov Y. SIAM Journal of Control and Optimization, 2004, no. 4(43), pp. 1253–1271.
  2. Levant A.IEEE 52nd Annual Conference on Decision and Control (CDC), 2013, рр. 4260–4265.
  3. Oza H.B., Orlov Y.V., Spurgeon S.K. 13th International Workshop on Variable Structure Systems (VSS), 2014, рр. 1–7. 
  4. Polyakov A., Efimov D., Perruquetti W. Proc. of 9th Symposium on Nonlinear Control Systems, 2013, рр. 140–145.
  5. Zimenko K.A., Polyakov A.E., Efimov D.V., Kremlev A.S. Journal of Instrument Engineering, 2015, no. 9(58), pp. 681–686. (in Russ.)
  6. Zimenko K.A., Polyakov A.E., Efimov D.V. Proceedings of the IEEE Conference on Decision and Control (CDC), 2016, рр. 4637–4641.
  7. Zubov V.I. Russian Mathematics, 1958, no. 1, pp. 80–88. (in Russ.)
  8. Bacciotti A., Rosier L. Lyapunov Functions and Stability in Control Theory, Springer, 2005, 237 p.