Approximate Reachability Analysis of Piecewise-Linear Dynamical Systems
In this paper we describe an experimental system called d/dt for approximating reachable states for hybrid systems whose continuous dynamics is defined by linear differential equations. We use an approximation algorithm whose accumulation of errors during the continuous evolution is much smaller than in previously-used methods. The d/dt system can, so far, treat non-trivial continuous systems, hybrid systems, convex differential inclusions and controller synthesis problems.
Unable to display preview. Download preview PDF.
- ABDPM00.E. Asarin, O. Bournez, T. Dang, A. Pnueli and O. Maler, Effective Synthesis of Switching Controllers for Linear Systems, submitted for publication, 2000.Google Scholar
- CV95.K. Cerans and J. Viksna, Deciding Reachability of Planar Multipolynomial systems, in R. Alur, T.A. Henzinger and E.D. Sontag (Eds.), Hybrid Systems III, 389–400, LNCS 1066, Springer, 1996.Google Scholar
- CC92.P. Cousot and R. Cousot, Abstract Interpretation and Application to Logic Programs, Journal of Logic Programming, 103–179, 1992.Google Scholar
- DM98.T. Dang, O. Maler, Reachability Analysis via Face Lifting, in T.A. Henzinger and S. Sastry (Eds), Hybrid Systems: Computation and Control, LNCS 1386, 96–109, Springer, 1998.Google Scholar
- G96.M.R. Greenstreet, Verifying Safety Properties of Differential Equations, in R. Alur and T.A. Henzinger (Eds.), Proc. CAV’96, LNCS 1102, 277–287, 1996.Google Scholar
- GM98.M.R. Greenstreet and I. Mitchell, Integrating Projections, in T.A. Henzinger and S. Sastry (Eds), Hybrid Systems: Computation and Control, LNCS 1386, 159–174, Springer, 1998.Google Scholar
- HHMW99.T.A. Henzinger, B. Horowitz, R. Majumdar, and H. Wong-Toi, Beyond HyTech: Hybrid System Analysis Using Interval Numerical Methods, AAAI Spring Symposium on Hybrid Systems, Stanford University, 1999.Google Scholar
- KV97.A. Kurzhanski and I. Valyi, Ellipsoidal Calculus for Estimation and Control, Birkhauser, 1997.Google Scholar
- MV99.K. Mehlhorn and St. Nher, The LEDA Platform of Combinatorial and Geometric Computing, Cambridge University Press, 1999.Google Scholar
- PLY99.G. Pappas, G. Lafierriere and S. Yovine, A New Class of Decidable Hybrid Systems, in J. van Schuppen (Eds.), Hybrid Systems: Computation and Control, LNCS 1569, Springer, 1999 [VS99] 29–31.Google Scholar
- PSK99.J. Preussig, O. Stursberg and S. Kowalewski, Reachability Analysis of a Class of Switched Continuous Systems by Integrating Rectangular Approximation and Rectangular Analysis, in J. van Schuppen (Eds.), Hybrid Systems: Computation and Control, LNCS 1569, Springer, 1999 [VS99] 208–222.Google Scholar
- V98.P. Varaiya, Reach Set Computation using Optimal Control, Proc. KIT Workshop, Verimag, Grenoble, 1998.Google Scholar