Mode Estimation of Probabilistic Hybrid Systems

  • Michael W. Hofbaur
  • Brian C. Williams
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2289)

Abstract

Model-based diagnosis and mode estimation capabilities excel at diagnosing systems whose symptoms are clearly distinguished from normal behavior. A strength of mode estimation, in particular, is its ability to track a system’s discrete dynamics as it moves between different behavioral modes. However, often failures bury their symptoms amongst the signal noise, until their effects become catastrophic. p] We introduce a hybrid mode estimation system that extracts mode estimates from subtle symptoms. First, we introduce a modeling formalism, called concurrent probabilistic hybrid automata (cPHA), that merge hidden Markov models (HMM) with continuous dynamical system models. Second, we introduce hybrid estimation as a method for tracking and diagnosing cPHA, by unifying traditional continuous state observers with HMM belief update. Finally, we introduce a novel, any-time, any-space algorithm for computing approximate hybrid estimates.

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References

  1. 1.
    Williams, B., Nayak, P.: A model-based approach to reactive self-configuring systems. In: Proc. of the 13th Nat. Conf. on Artificial Intelligence (AAAI-96). (1996)Google Scholar
  2. 2.
    Anderson, B., Moore, J.: Optimal Filtering. Prentice Hall (1979)Google Scholar
  3. 3.
    Branicky, M.: Studies in Hybrid Systems: Modeling, Analysis, and Control. PhD thesis, Department of Electrical Engineering and Computer Science, MIT (1995)Google Scholar
  4. 4.
    Henzinger, T.: The theory of hybrid automata. In: Proc. of the 11th Annual IEEE Symposium on Logic in Computer Science (LICS’ 96) (1996) 278–292Google Scholar
  5. 5.
    Hu, J., Lygeros, J., Sastry, S.: Towards a theory of stochastic hybrid systems. In Lynch, N., Krogh, B., eds.: Hybrid Systems: Computation and Control. Lecture Notes in Computer Science, 1790. Springer (2000) 160–173CrossRefGoogle Scholar
  6. 6.
    Nancy Lynch, Roberto Segala, F.V.: Hybrid I/O automata revisited. In M.D. Di Benedetto, A.S.V., ed.: Hybrid Systems: Computation and Control, HSCC 2001. Lecture Notes in Computer Science, 2034. Springer Verlag (2001) 403–417CrossRefGoogle Scholar
  7. 7.
    Maybeck, P., Stevens, R.: Reconfigurable flight control via multiple model adaptive control methods. IEEE Transactions on Aerospace and Electronic Systems 27 (1991) 470–480CrossRefGoogle Scholar
  8. 8.
    Bar-Shalom, Y., Li, X.: Estimation and Tracking. Artech House (1993)Google Scholar
  9. 9.
    Li, X., Bar-Shalom, Y.: Multiple-model estimation with variable structure. IEEE Transactions on Automatic Control 41 (1996) 478–493MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    McIlraith, S., Biswas, G., Clancy, D., Gupta, V.: Towards diagnosing hybrid systems. In: Proc. of the 10th Internat. Workshop on Principles of Diagnosis. (1999) 194–203Google Scholar
  11. 11.
    Narasimhan, S., Biswas, G.: Efficient diagnosis of hybrid systems using models of the supervisory controller. In: Proc. of the 12th Internat. Workshop on Principlesof Diagnosis. (2001) 127–134Google Scholar
  12. 12.
    Zhao, F., Koutsoukos, X., Haussecker, H., Reich, J., Cheung, P.: Distributed monitoringof hybrid systems: A model-directed approach. In: Proc. of the Internat. Joint Conf. on Artificial Intelligence (IJCAI’01). (2001) 557–564Google Scholar
  13. 13.
    Lerner, U., Parr, R., Koller, D., Biswas, G.: Bayesian fault detection and diagnosis in dynamic systems. In: Proc. of the 17th Nat. Conf. on Artificial Intelligence (AAAI’00). (2000)Google Scholar
  14. 14.
    McIlraith, S.: Diagnosing hybrid systems: a Bayseian model selection approach. In: Proc. of the 11th Internat. Workshop on Principles of Diagnosis. (2000) 140–146Google Scholar
  15. 15.
    Robert, C., Casella, G.: Monte Carlo Statistical Methods. Springer-Verlag (1999)Google Scholar
  16. 16.
    Hanlon, P., Maybeck, P.: Multiple-model adaptive estimation using a residual correlation Kalman filter bank. IEEE Transactions on Aerospace and Electronic Systems 36 (2000) 393–406CrossRefGoogle Scholar
  17. 17.
    Williams, B., Millar, B.: Decompositional, model-based learning and its analogy to diagnosis. In: Proc. of the 15th Nat. Conf. on Artificial Intelligence (AAAI-98). (1998)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Michael W. Hofbaur
    • 1
    • 2
  • Brian C. Williams
    • 1
  1. 1.MIT Space Systems and Artificial Intelligence LaboratoriesCambridgeUSA
  2. 2.Department of Automatic ControlGraz University of TechnologyGrazAustria

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