Summary
This chapter presents optimal supervisory control of dynamical systems that can be represented by deterministic finite state automaton (DFSA) models. The performance index for the optimal policy is obtained by combining a measure of the supervised plant language with (possible) penalty on disabling of controllable events. The signed real measure quantifies the behavior of controlled sublanguages based on a state transition cost matrix and a characteristic vector as reported in Chapter 1 and earlier publications. Synthesis of the optimal control policy requires at most n iterations, where n is the number of states of the DFSA model generated from the unsupervised plant language. The computational complexity of the optimal control synthesis is polynomial in n. Syntheses of the control algorithms are illustrated with two application examples.
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References
Y. Brave and M. Heyman, On optimal attraction of discrete-event processes, Information Science 67 (1993), no. 3, 245–276.
J. Fu, C.M. Lagoa, and A. Ray, Robust optimal control of regular languages with event cost uncertainties, Proceedings of IEEE Conference on Decision and Control, December 2003, pp. 3209–3214.
J. Fu, A. Ray, and C.M. Lagoa, Optimal control of regular languages with event disabling cost, Proceedings of American Control Conference, Denver, Colorado, June 2003, pp. 1691–1695.
J. Fu, A. Ray, and C.M. Lagoa, Unconstrained optimal control of regular languages, Automatica 40 (2004), no. 4, 639–648.
R. Kumar and V. Garg, Optimal supervisory control of discrete event dynamical systems, SIAM J. Control and Optimization 33 (1995), no. 2, 419–439.
A.W. Naylor and G.R. Sell, Linear operator theory in engineering and science, Springer-Verlag, 1982.
K. Passino and P. Antsaklis, On the optimal control of discrete event systems, Proceedings of 28th IEEE Decision and Control Conference, Tampa, Florida (1989), 2713–2718.
P.J. Ramadge and W.M. Wonham, Supervisory control of a class of discrete event processes, SIAM J. Control and Optimization 25 (1987), no. 1, 206–230.
A. Ray and S. Phoha, Signed real measure of regular languages for discrete-event automata, Int. J. Control 76 (2003), no. 18, 1800–1808.
R. Sengupta and S. Lafortune, An optimal control theory for discrete event systems, SIAM J. Control and Optimization 36 (1998), no. 2, 488–541.
A. Surana and A. Ray, Signed real measure of regular languages, Demonstratio Mathematica 37 (2004), no. 2, 485–503.
X. Wang and A. Ray, A language measure for performance evaluation of discrete-event supervisory control systems, Applied Mathematical Modelling 28 (2004), no. 9, 817–833.
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Ray, A., Fu, J., Lagoa, C. (2005). Optimal Supervisory Control of Regular Languages. In: Ray, A., Phoha, V.V., Phoha, S.P. (eds) Quantitative Measure for Discrete Event Supervisory Control. Springer, New York, NY. https://doi.org/10.1007/0-387-23903-0_2
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DOI: https://doi.org/10.1007/0-387-23903-0_2
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