Abstract
We analyse a switching control system for controlling a plant with unknown parameters so that the output asymptotically tracks a reference signal. The controller is selected on-line from a given set of controllers according to a switching rule based on output prediction errors. We provide sufficient conditions under which the switched closed loop control system is exponentially stable and asymptotically achieves good tracking control even if the switching does not stop.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This work was supported in part by the National Science Foundation under grants IRI-9457645 and ECS-9216450, and by EPRI under grant RP8030-18.
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
Shankar Sastry and Mark Bodson, Adaptive Control: Stability, Convergence, and Robustness, Prentice Hall, Englewood Cliffs, New Jersey, 1989.
K. Ciliz and K. Narendra, Multipole model based adaptive control of robotic manipulators, Proc. of the 33rd IEEE conference on Decision and Control, pp. 1305–1310, 1994.
W. A. Coppel, Dichotomies in stability theory, Lecture Notes in Mathematics No. 629, Springer, 1978.
C. A. Desoer, Slowly varying system \(\dot x = A(t)x\), IEEE Trans. on Automatic Control, pp. 780–781, Dec. 1969.
M. Fu and B. R. Barmish, Adaptive stabilization of linear systems via switching controls, IEEE Trans. on Automatic Control, pp. 1079–1103, Dec. 1986.
J. Hocherman-Frommer, S. R. Kulkarni, P. J. Ramadge, “Controller switching based on output prdiction errors,” To appear IEEE Transactions on Automatic Control, May 1998.
A. Ilchmann, D. H. Owens and D. Pratzel-Walters, “Sufficient conditions for stability of linear time varying systems,” Systems & Control Letters, No. 9, pp. 157–163, 1987.
S. Kulkarni and P. J. Ramadge, “Model and controller selection policies based on output prediction errors,” IEEE Transactions on Automatic Control, November 1996.
S. Kulkarni and P. J. Ramadge, “Prediction error based controller selection policies,” IEEE Conference on Decision and Control, New Orleans, Dec. 1995.
B. Mårtensson, “The order of any stabilizing regulator is sufficient a priori information for adaptive stabilization,” Systems and Control Letters, Vol. 6, No. 2, pp. 87–91, 1985.
D. E. Miller, “Adaptive stabilization using a nonlinear time-varying controller,” IEEE Trans. on Automatic Control, 39 (7), pp. 1347–1359, July 1994.
A. S. Morse, D. Q. Mayne, and G. C. Goodwin, “Applications of hysteresis switching in parameter adaptive control,” IEEE Trans. Automatic Control, 37 (9), pp. 1343–1354, Setp. 1992.
A. S. Morse, Supervisory control of families of linear set-point controllers, Proc. of the 32nd IEEE conference on Decision and Control, pp.1055–1060, 1993.
A. S. Morse, “Supervisory control of families of linear set-point controllers — part 1: exact matching,” preprint, March 1993.
A. S. Morse, “Control using logic-based switching,” Proc. of 1995 European Control Conference, Rome, Italy, Sept. 1995.
K. Narendra and J. Balakrishnan, “Improving transient response of adaptive control systems using multiple models and switching,” Proc. of the 32rd IEEE Conf. on Decision and Control, San Antonio, Texas, Dec. 1993.
K. Narendra and J. Balakrishnan, “Intelligent control using fixed and adaptive models,” Proc. of the 33rd IEEE Conf. on Decision and Control, pp. 1680–1685, Lake Buena Vista, Florida, Dec. 1994.
V. Solo, “On the stability of slowly time-varying linear systems,” Mathematics of Control, Signals and Systems, No. 7, pp. 331–350, 1994.
S. R. Weller and G. C. Goodwin, “Hysteresis switching adaptive control of linear multivariable systems,” IEEE Trans. Automatic Control, 39 (7), pp. 1360–1375, July 1994.
W. M. Wonham, Linear Multivariable Control: a Geometric Approach, Second Ed., Springer-Verlag, New York, 1979.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1999 Springer-Verlag London Limited
About this paper
Cite this paper
Hocherman-Frommer, J., Kulkarni, S.R., Ramadge, P.J. (1999). Controller switching based on output predictions. In: Yamamoto, Y., Hara, S. (eds) Learning, control and hybrid systems. Lecture Notes in Control and Information Sciences, vol 241. Springer, London. https://doi.org/10.1007/BFb0109726
Download citation
DOI: https://doi.org/10.1007/BFb0109726
Published:
Publisher Name: Springer, London
Print ISBN: 978-1-85233-076-7
Online ISBN: 978-1-84628-533-2
eBook Packages: Springer Book Archive