Abstract
In this paper we introduce and study the notion of safety control of stochastic discrete event systems (DESs), modeled as controlled Markov chains. For non-stochastic DES’s, modeled by state machines or automata, safety is specified as a set of forbidden states, or equivalently by a binary valued vector that imposes an upper bound on the set of states permitted to be visited. We generalize this notion of safety to the setting of stochastic DESs by specifying it as an unit-interval valued vector that imposes an upper bound on the state probability distribution vector. Under the assumption of complete state observation, we identify (i) the set of all state feedback controllers that satisfy the safety requirement for any given safe initial state probability distribution, and (ii) the set of all safe initial state probability distributions for a given state feedback controller.
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References
Bertsekas, D. (1987). Dynamic Programming: Deterministic and Stochastic Models. Prentice Hall, Inc., Englewood Cliffs, NJ.
Garg, V. K., Kumar, R., and Marcus, S. I. (1999). A probabilistic language formalism for stochastic discrete event systems. IEEE Transactions on Automatic Control, 44(2):280–293.
Gunnarsson, J. (1997). Symbolic methods and tools for discrete event dynamic systems. PhD thesis, Linkoping University, Linkping, Sweden.
Holloway, L. E., Krogh, B. H., and Giua, A. (1997). A survey of Petri net methods for controlled discrete event systems. Journal of Discrete Event Dynamical Systems: Theory and Applications, 7(2): 151–190.
Kumar, P. R. and Varaiya, P. (1986). Stochastic Systems: Estimation, identification and adaptive control. Prentice Hall.
Kumar, R. and Garg, V. K. (1998a). Control of stochastic discrete event systems: Existence. In Proceedings of 1998 International Workshop on Discrete Event Systems, Cagliari, Italy.
Kumar, R. and Garg, V. K. (1998b). Control of stochastic discrete event systems: Synthesis. In 1998 IEEE Conference on Decision and Control, Tampa, FL.
Kumar, R., Garg, V. K., and Marcus, S. I. (1993). Predicates and predicate transformers for supervisory control of discrete event systems. IEEE Transactions on Automatic Control, 38(2):232–247.
Ramadge, P. J. and Wonham, W. M. (1987). Supervisory control of a class of discrete event processes. SIAM Journal of Control and Optimization, 25(l):206–230.
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© 2000 Springer Science+Business Media New York
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Arapostathis, A., Kumar, R., Tangirala, S. (2000). Safety Control of Completely Observed Markov Chains. In: Boel, R., Stremersch, G. (eds) Discrete Event Systems. The Springer International Series in Engineering and Computer Science, vol 569. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-4493-7_44
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DOI: https://doi.org/10.1007/978-1-4615-4493-7_44
Publisher Name: Springer, Boston, MA
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