Abstract
In previous work we demonstrated that reachability algorithms using level set methods and based on the Hamilton-Jacobi PDE can be adapted to systems whose dynamics are described by differential algebraic equations. Here we extend those results to hybrid systems. The only significant addition required is a mechanism for handling the state reset that occurs during discrete jumps between modes. We demonstrate the technique on a nonlinear power system voltage safety problem.
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Mitchell, I.M.: Comparing forward and backward reachability as tools for safety analysis. In: Bemporad, A., Bicchi, A., Buttazzo, G. (eds.) HSCC 2007. LNCS, vol. 4416, pp. 428–443. Springer, Heidelberg (2007)
Cross, E.A., Mitchell, I.M.: Level set methods for computing reachable sets of systems with differential algebraic equation dynamics. In: Proceedings of the American Control Conference, Seattle, WA (2008), http://www.cs.ubc.ca/~mitchell/Papers/submittedReachDAE.pdf
[Online], http://www.cs.ubc.ca/~mitchell/ToolboxLS
Tomlin, C., Mitchell, I., Bayen, A., Oishi, M.: Computational techniques for the verification of hybrid systems. Proceedings of the IEEE 91(7), 986–1001 (2003)
Venkatasubramanian, V., Schättler, H., Zaborszky, J.: Voltage dynamics: Study of a generator with voltage control, transmission, and matched MW load. IEEE Transactions on Automatic Control 37(11), 1717–1733 (1992)
Susuki, Y., Hikihara, T.: Predicting voltage instability of power system via hybrid system reachability analysis. In: Proceedings of the American Control Conference, New York, NY, pp. 4166–4171 (2007)
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Mitchell, I.M., Susuki, Y. (2008). Level Set Methods for Computing Reachable Sets of Hybrid Systems with Differential Algebraic Equation Dynamics. In: Egerstedt, M., Mishra, B. (eds) Hybrid Systems: Computation and Control. HSCC 2008. Lecture Notes in Computer Science, vol 4981. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78929-1_51
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DOI: https://doi.org/10.1007/978-3-540-78929-1_51
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-78928-4
Online ISBN: 978-3-540-78929-1
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