Abstract
Hybrid control systems (HCS) arise when the plant, a continuous state system (CSS), is controlled by a discrete event system (DES) controller. It is assumed that there exists a specification on the plant's desired symbolic behaviour. This specification describes how various operational modes of the controlled plant should fit together. One design problem involves determining an HCS that “realizes” the specified behaviour in a “stable” manner. In this paper, a solution is posed which involves finding a sequence of subgoals and controllers achieving the specified behaviour in a “logically” stable manner. The solution can therefore be viewed as a “logically” stable extension of the previously given symbolic specification on the plant's behaviour. This paper shows how such an extension can be constructed using multiple H ∞ control agents exhibiting robust stability. The problem formulation leads to a design problem which can be solved using existing H ∞ control techniques.
The authors gratefully acknowledge the partial financial support of the National Science Foundation (MSS92-16559) and the Electric Power Research Institute (RP8030-06).
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
R.L. Grossman, A. Nerode, A.P. Ravn, and H. Rischel (eds.), Hybrid Systems, Lecture Notes in Computer Science 736, Springer Verlag, 1993.
A. Benveniste and P. Le Guernic, “Hybrid dynamical systems and the signal language”, IEEE Transactions on Automatic Control, Vol. 35, No. 5, pp 535–546, May 1990.
A. Gollu and P. Varaiya, “Hybrid dynamical systems”, In Proceedings of the 28th Conference on Decision and Control, pp. 2708–2712, Tampa, FL, Dec. 1989.
L.Holloway and B. Krogh, “Properties of behavioural models for a class of hybrid dynamical systems”, In Proceedings of the 31st Conference on Decision and Control, pp. 3752–2757, Tuscon, AZ, Dec. 1992.
K.M. Passino and U. Ozguner, “Modeling and analysis of hybrid systems: examples”, In Proceedings of the 1991 IEEE International Symposium on Intelligent Control, pp. 251–256, Arlington, VA, Aug. 1991.
P. Peleties and R. DeCarlo, “A modeling strategy with event structures for hybrid systems”, In Proceedings of the 28th Conference on Decision and Control, pp. 1308–1313, Tampa, FL, Dec. 1989.
P.J. Ramadge, “On the periodicity of symbolic observations of piecewise smooth discrete-time systems”, IEEE Transactions on Automatic Control, Vol. 35, No. 7, pp. 807–812, July 1990.
M.D. Lemmon and P.J. Antsaklis, “Inductively Inferring Valid Logical Models of Continuous-State Dynamical Systems”, Theoretical Computer Science, 138 (1995) 201–210.
M.D. Lemmon and P.T. Szymanski, “Interior point implementations of alternating minimization training”, to appear in Advances in Neural Information Processing Systems 7, pp. 574–582, San Mateo, California: Morgan Kaufmann publishers, 1995.
P.T. Szymanski, and M.D. Lemmon, “A modified interior point method for supervisory controller design”, in Proceedings of the 33rd IEEE Conference on Decision and Control, Orlando Florida, pp. 1381–1386, December, 1994.
P. Antsaklis, J. Stiver, and M. Lemmon, “Hybrid system modeling and autonomous control systems”, in [1], pp. 366–392. Springer-Verlag, 1993.
A. Nerode and W. Kohn, “Multiple agent hybrid control architecture”, in [1], pp. 297–316, Springer-Verlag, 1993.
J.A. Stiver and P.J. Antsaklis, “Modeling and analysis of hybrid control systems”, In Proceedings of the 31st Conference on Decision and Control, pp. 3748–3751, Tuscon, AZ, Dec. 1992.
A. Nerode and W. Kohn, “Models for hybrid systems: automata, topologies, controllability, observability”, in [1],pp. 317–356, Springer Verlag, 1993.
R.W. Brockett, “Hybrid models for motion control systems”, Technical Report CICSP-364, Center for Intelligent Control Systems, Massachusetts Institute of Technology, March 1993.
M.S. Branicky, V.S. Borkar, and S.K. Mitter, “A unified framework for hybrid control: background, model, and theory”, Technical Report LIDS-P-2239, Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, April 1994.
W.H. Fleming and R.W. Rishel, Deterministic and Stochastic Optimal Control, Springer Verlag, 1975.
M. Groetschel, L. Lovasz and A. Schrijver, Geometric Algorithms and Combinatorial Optimization. Springer-Verlag, Berlin, 1988.
J.S. Shamma, and M. Athans, “Analysis of gain scheduled control for nonlinear plants”, IEEE Trans. on Automatic Control, Vol. AC-35, No. 8, pp. 898–907, August 1990.
S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear matrix inequalities in system and control theory, SIAM Studies in Applied Mathematics vol 15, 1994.
C.C. Gonzaga (1992), “Path-Following Methods for Linear Programming”, SIAM Review, Vol 34(2), pp. 167–224, June 1992.
M.D. Lemmon, P.T. Szymanski, and C.Bett, “Interior point competitive learning of control agents in colony-style systems”, to appear in Proceedings of SPIE Orlando Symposium, Volume 2492, April 1995.
L.C. Young, Optimal Control Theory, Chelsea Publishing Co. NY 1980.
W. Kuich and A. Salomaa, Semirings, automata, and languages, Springer Verlag, 1985.
X. Ge, W.Kohn, and A. Nerode, “Algorithms for chattering approximations to relaxed optimal controls”, Technical Report 94-23, Mathematical Sciences Institute, Cornell University, April 1994.
J. Doyle, A. Packard, and K. Zhou, “Review of LFTs, LMIs and Μ”, Proceedings of the 30th Conference on Decision and Control, Brighton, England, Dec 1991.
K. Glover, “Multiplicative approximation of linear multivariable systems with L ∞ error bounds”, in Proceedings of the American Control Conference, pp. 1705–1709, 1986.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1995 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Lemmon, M., Bett, C., Szymanski, P., Antsaklis, P. (1995). Constructing hybrid control systems from robust linear control agents. In: Antsaklis, P., Kohn, W., Nerode, A., Sastry, S. (eds) Hybrid Systems II. HS 1994. Lecture Notes in Computer Science, vol 999. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60472-3_16
Download citation
DOI: https://doi.org/10.1007/3-540-60472-3_16
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-60472-3
Online ISBN: 978-3-540-47519-4
eBook Packages: Springer Book Archive