Abstract
This paper addresses the question of extending the usual approximation and sampling theory of continuous signals and systems to those encompassing discontinuities, such as found in modern distributed control systems. We provide a topological framework dealing with continuous, discrete and mixed systems in a uniform manner. We show how this theoretical framework can be used for voting on hybrid signals in critical real-time systems.
This work has been supported by the European Network of Excellence Artist and by the Airbus-Verimag CIFRE grant 2003-2006.
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References
Chutinan, A., Krogh, B.H.: Computing approximating automata for a class of hybrid systems. Mathematical and Computer Modeling of Dynamical Systems 6, 30–50 (2000); Special Issue on Discrete Event Models of Continuous Systems
Avizienis, A.: The methodology of n-version programming. In: Lyu, M.R. (ed.) Software Fault Tolerance, pp. 23–46. John Wiley, Chichester (1995)
Billingsley, P.: Convergence of probability measures. John Wiley & Sons, Chichester (1999)
Branicky, M.S.: Topology of hybrid systems. In: 32nd Conference on Decision and Control, pp. 2309–2311. IEEE, Los Alamitos (1993)
Caspi, P., Benveniste, A.: Toward an approximation theory for computerised control. In: Sangiovanni-Vincentelli, A.L., Sifakis, J. (eds.) EMSOFT 2002. LNCS, vol. 2491, Springer, Heidelberg (2002)
Caspi, P., Mazuet, C., Salem, R., Weber, D.: Formal design of distributed control systems with Lustre. In: Felici, M., Kanoun, K., Pasquini, A. (eds.) SAFECOMP 1999. LNCS, vol. 1698, Springer, Heidelberg (1999)
Caspi, P., Salem, R.: Threshold and bounded-delay voting in critical control systems. In: Joseph, M. (ed.) FTRTFT 2000. LNCS, vol. 1926, pp. 68–81. Springer, Heidelberg (2000)
Asarin, E., Maler, O., Pnueli, A.: On discretization of delays in timed automata and digital circuits. In: Sangiorgi, D., de Simone, R. (eds.) CONCUR 1998. LNCS, vol. 1466, pp. 470–484. Springer, Heidelberg (1998)
Gupta, V., Henzinger, T.A., Jagadeesan, R.: Robust timed automata. In: Maler, O. (ed.) HART 1997. LNCS, vol. 1201, pp. 331–345. Springer, Heidelberg (1997)
Ouaknine, J.: Digitisation and full abstraction for dense-time model checking. In: Katoen, J.-P., Stevens, P. (eds.) ETAPS 2002 and TACAS 2002. LNCS, vol. 2280, pp. 37–51. Springer, Heidelberg (2002)
Kopetz, H.: Real-Time Systems Design Principles for Distributed Embedded Applications. Kluwer, Dordrecht (1997)
Kossentini, C., Caspi., P.: Mixed delay and threshold voters in critical real-time systems. In: Lakhnech, Y., Yovine, S. (eds.) FORMATS 2004 and FTRTFT 2004. LNCS, vol. 3253, Springer, Heidelberg (2004)
Kossentini, C., Caspi, P.: Approximation, sampling and voting in hybrid computing systems. Research Report TR-2005-19, Verimag (December 2005), Available at: http://www-verimag.imag.fr/TR/TR-2005-17.pdf
Broucke, M.: Regularity of solutions and homotopic equivalence for hybrid systems. In: Proceedings of the 37th IEEE Conference on Decision and Control, vol. 4, pp. 4283–4288 (1998)
Alur, R., Henzinger, T.A., Lafferriere, G., Pappas, G.J.: Discrete abstractions of hybrid systems. Proceedings of the IEEE 88, 971–984 (2000)
Wensley, J.H., Lamport, L., Goldberg, J., Green, M.W., Lewitt, K.N., Melliar-Smith, P.M., Shostak, R.E.: SIFT: Design and analysis of a fault-tolerant computer for aircraft control. Proceedings of the IEEE 66(10), 1240–1255 (1978)
Kohn, W., Nerode, A.: Models for hybrid systems: automata, topologies, controllability and observability. In: Dal Cin, M., Bode, A. (eds.) Parallel Computer Architectures. LNCS, vol. 732, Springer, Heidelberg (1993)
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Kossentini, C., Caspi, P. (2006). Approximation, Sampling and Voting in Hybrid Computing Systems. In: Hespanha, J.P., Tiwari, A. (eds) Hybrid Systems: Computation and Control. HSCC 2006. Lecture Notes in Computer Science, vol 3927. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11730637_28
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DOI: https://doi.org/10.1007/11730637_28
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-33170-4
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