A Second-Order Approximation for DEVS Simulation of Continuous Systems

Abstract

In this article, based on the methodology of discrete event simulation of continuous systems via quantized state systems (QSS), a new second-order approximation, called second-order quantized state systems (QSS2), is proposed. This new approximation, which satisfies the same stability and convergence properties that were deduced for QSS in previous works, also allows reducing the number of calculations with respect to the former method. It is shown that in the particular case of linear time-invariant (LTI) systems, the QSS2 can be exactly represented by a DEVS model, and in nonlinear systems, an approximated DEVS model can be also obtained. For the LTI case, a closed formula giving the necessary quantization that allows achieving a bound in the error during the whole simulation is deduced. This formula, which stands for both QSS and QSS2 approaches, also proves that for any quantization, the error is always bounded.

Keywords

Simulation of ODEs discrete event simulation DEVS quantized state systems

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References

Press, W. , B. Flannery , S. Teukolsky , and W. Vetterling . 1986. Numerical recipes. Cambridge, UK: Cambridge University Press.

Zeigler, B. 1976. Theory of modeling and simulation. New York: John Wiley.

Zeigler, B. , T. Kim , and H. Praehofer . 2000. Theory of modeling and simulation. 2d ed. New York: Academic Press.

Zeigler, B. , and J. Lee . 1998. Theory of quantized systems: Formal basis for DEVS/HLA distributed simulation environment. In SPIE Proceedings, pp. 49-58.

Kofman, E. , and S. Junco . 2001. Quantized state systems: A DEVS approach for continuous system simulation. Transactions of SCS 18 (3):123-132.

Kofman, E. , and S. Junco . 2001. Quantized bond graphs: An approach for discrete event simulation of physical systems. In Proceedings of ICBGM’01, Phoenix, AZ, pp. 369-374.

Giambiasi, N. , B. Escude , and S. Ghosh . 2000. GDEVS: A generalized discrete event specification for accurate modeling of dynamic systems. Transactions of SCS 17 (3): 120-134.

Kofman, E. , J. Lee , and B. Zeigler . 2001. DEVS representation of differential equation systems: Review of recent advances. In Proceedings of ESS’01, October, Marseille, France.

Ismail, Y. , E. Friedman , and J. Neves . 1999. Figures of merit to characterize the importance of on-chip inductance. IEEE Transactions on VLSI Systems 7 (4): 442-449.

10.

Brockett, R. , and D. Liberzon . 2000. Quantized feedback stabilization of linear systems. IEEE Trans. Automat. Contr. 45:1279-1289.

11.

Wainer, G. 2000. Improved cellular models with parallel cell DEVS. Transactions of SCS 17 (2): 73-88.