Accurate hybridization of nonlinear systems

HSCC'10 - Proceedings of the 13th ACM International Conference on Hybrid Systems: Computation and Control

Volumn , Issue , 2010, Pages 11-19

  Dang, Thao ^a   Maler, Oded ^a   Testylier, Romain ^a  

^a VERIMAG   (France)

Author keywords

Formal verication; Non linear systems; Numerical analysis; Reachability computation

Indexed keywords

FORMAL VERICATION; FUNCTION APPROXIMATION; HIGH-DIMENSIONAL; INTERPOLATION ERROR; NON-LINEAR; PERFORMANCE IMPROVEMENTS; REACHABILITY; REACHABLE SET; SMALL REGION; STATE SPACE; TIME EFFICIENCIES; VECTOR FIELDS;

ELECTRIC GROUNDING; HYBRID COMPUTERS; HYBRID SYSTEMS; INTERPOLATION; LINEAR SYSTEMS; VECTOR SPACES;

NONLINEAR SYSTEMS;

EID: 77953058505     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1755952.1755956     Document Type: Conference Paper

References (21)

1. M. Althoff, O. Stursberg, and M. Buss. Reachability Analysis of Nonlinear Systems with Uncertain Parameters using Conservative Linearization. Conference on Decision and Control CDC'08, 2008.
2. E. Asarin, O. Bournez, T. Dang, and O. Maler. Approximate reachability analysis of piecewise linear dynamical systems, Hybrid Systems: Computation and Control HSCC'00, LNCS 1790, 21-31, 2000.
3. Eugene Asarin, Thao Dang, and Antoine Girard. Reachability Analysis of Nonlinear Systems Using Conservative Approximation. Hybrid Systems: Computation and Control HSCC'03, LNCS 2623, pp 20-35, Springer, 2003.
4. E. Asarin, T. Dang, and A. Girard. Hybridization Methods for the Analysis of Nonlinear Systems, Acta Informatica 43, 451-476, 2007.
5. A. Chutinan and B.H. Krogh. Computational Techniques for Hybrid System Verification. IEEE Trans. on Automatic Control 48, 64-75, 2003.
6. T. Dang, C. Le Guernic, and O. Maler. Computing Reachable States for Nonlinear Biological Models. Computational Methods in Systems Biology CMSB'09, LNCS 5688, pp 126-141, Springer, 2009.
7. T. Dang. Approximate Reachability Computation for Polynomial Systems, Hybrid Systems: Control and Computation HSCC'06, LNCS 3927, pp 138-152, Springer, 2006.
8. J. Della Dora, A. Maignan, M. Mirica-Ruse, and S. Yovine. Hybrid computation. Proceedings International Symposium on Symbolic and Algebraic Computation ISSAC'01, 2001.
9. D. Du and F. Hwang. Computing in Euclidean geometry World Scientific (Singapore, River Edge, N.J), 1992.
10. A. Girard, Reachability of Uncertain Linear Systems using Zonotopes, Hybrid Systems: Control and Computation HSCC'05, LNCS 3414, 291-305, Springer, 2005.
11. A. Girard, C. Le Guernic and O. Maler, Efficient Computation of Reachable Sets of Linear Time-invariant Systems with Inputs. Hybrid Systems: Control and Computation HSCC'06, LNCS 3927, 257-271 2006.
12. M.R. Greenstreet and I. Mitchell, Reachability Analysis Using Polygonal Projections, Hybrid Systems: Control and Computation HSCC'99 LNCS 1569, 103-116, Springer, 1999.
13. E.D. Karagiannis and A.S. Popel. A theoretical model of type I collagen proteolysis by matrix metalloproteinase (MMP) 2 and membrane type 1 MMP in the presence of tissue inhibitor of metalloproteinase 2 The Journal of Biological Chemistry, 279:37, pp 39106-39114, 2004.
14. M. Kloetzer and C. Belta, Reachability analysis of multi-affine systems. Hybrid Systems: Computation and Control HSCC'06, LNCS 3927, 348-362, Springer, 2006.
15. A. Kurzhanskiy and P. Varaiya, Ellipsoidal Techniques for Reachability Analysis of Discrete-time Linear Systems, IEEE Trans. Automatic Control 52, 26-38, 2007. (Pubitemid 46343995)
16. M. Kvasnica, P. Grieder, M. Baotic, and Manfred Morari. Multi-Parametric Toolbox (MPT) Hybrid Systems: Computation and Control HSCC'04, LNCS 2993, pp 448-462, Springer, 2004.
17. I. Mitchell and C. Tomlin. Level Set Methods for Computation in Hybrid Systems, Hybrid Systems: Computation and Control HSCC'00, LNCS 1790, 310-323, 2000.
18. J.R. Shewchuk. What Is a Good Linear Element? Interpolation, Conditioning, and Quality Measures. Eleventh International Meshing Roundtable (Ithaca, New York), pp 115-126, Sandia National Laboratories, September 2002.
19. A. Tiwari and G. Khanna. Nonlinear Systems: Approximating Reach Sets. Hybrid Systems: Computation and Control HSCC'04, LNCS 2993, pp 600-614, 2004.
20. P. Varaiya, Reach Set computation using Optimal Control, KIT Workshop, Verimag, Grenoble, 377-383, 1998.
21. S. Waldron. The error in linear interpolation at the vertices of a simplex. SIAM J. Numer. Anal., 35(3), 1191-1200, (1998).