Image computation for polynomial dynamical systems using the bernstein expansion

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 5643 LNCS, Issue , 2009, Pages 219-232

  Dang, Thao ^a   Salinas, David ^a  

^a VERIMAG   (France)

Author keywords

[No Author keywords available]

Indexed keywords

CONTINUOUS DYNAMICS; ENGINEERING DOMAINS; IMAGE COMPUTATION; ONE STEP; POLYNOMIAL DYNAMICAL SYSTEMS; POLYNOMIAL FUNCTIONS; PRACTICAL SYSTEMS; PROTOTYPE IMPLEMENTATIONS; SET-BASED ANALYSIS;

AMBER; COMPUTER AIDED ANALYSIS; DIFFERENCE EQUATIONS; EMBEDDED SOFTWARE; EMBEDDED SYSTEMS; HYBRID SYSTEMS; MILITARY PHOTOGRAPHY; POLYNOMIALS; SOFTWARE PROTOTYPING;

SET THEORY;

EID: 70350247889     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-02658-4_19     Document Type: Conference Paper

References (25)

1. Asarin, E., Dang, T., Girard, A.: Hybridization methods for the analysis of nonlinear systems. Acta Informatica 43(7), 451-476 (2007)
2. Boyd, S., Vandenberghe, S.: Convex optimization. Cambridge Uni. Press, Cambridge (2004)
3. Clauss, F., Yu, C.I.: Application of symbolic approach to the Bernstein expansion for program analysis and optimization. Program. Comput. Softw. 30(3), 164-172 (2004)
4. Dang, T.: Approximate reachability computation for polynomial systems. In: Hespanha, J.P., Tiwari, A. (eds.) HSCC 2006. LNCS, vol. 3927, pp. 138-152. Springer, Heidelberg (2006)
5. Dang, T., Salinas, D.: Computing set images of polynomias. Technical report, VERIMAG (June 2008)
6. Fotiou, I.A., Rostalski, P., Parrilo, P.A., Morari, M.: Parametric optimization and optimal control using algebraic geometriy methods. Int. Journal of Control 79(11), 1340-1358 (2006)
7. Garloff, J.: Application of Bernstein expansion to the solution of control problems. University of Girona, pp. 421-430 (1999)
8. Garloff, J., Jansson, C., Smith, A.P.: Lower bound functions for polynomials. Journal of Computational and Applied Mathematics 157, 207-225 (2003)
9. Garloff, J., Smith, A.P.: An improved method for the computation of affine lower bound functions for polynomials. In: Frontiers in Global Optimization. Series Nonconvex Optimization and Its Applications. Kluwer Academic Publ., Dordrecht (2004)
10. Garloff, J., Smith, A.P.: A comparison of methods for the computation of affine lower bound functions for polynomials. In: Jermann, C., Neumaier, A., Sam, D. (eds.) COCOS 2003. LNCS, vol. 3478, pp. 71-85. Springer, Heidelberg (2005)
11. Girard, A., Le Guernic, C., Maler, O.: Efficient Computation of Reachable Sets of Linear Time-Invariant Systems with Inputs. In: Hespanha, J.P., Tiwari, A. (eds.) HSCC 2006. LNCS, vol. 3927, pp. 257-271. Springer, Heidelberg (2006)
12. He, F., Yeung, L.F., Brown, M.: Discrete-time model representation for biochemical pathway systems. IAENG Int. Journal of Computer Science 34(1) (2007)
13. Henrion, D., Lasserre, J.B.: Gloptipoly: Global optimization over polynomials with matlab and sedumi. In: Proceedings of CDC (2002)
14. Jolliffe, I.T.: Principal Component Analysis. Springer, Heidelberg (2002)
15. Jordan, D.W., Smith, P.: Nonlinear Ordinary Differential Equations. Oxford Applied Mathematics and Computer Science. Oxford Uni. Press, Oxford (1987)
16. Mourrain, B., Pavone, J.P.: Subdivision methods for solving polynomial equations. Technical report, INRIA Research report, 5658 (August. 2005)
17. Platzer, A., Clarke, E.M.: The Image Computation Problem in Hybrid Systems Model Checking. In: Bemporad, A., Bicchi, A., Buttazzo, G. (eds.) HSCC 2007. LNCS, vol. 4416, pp. 473-486. Springer, Heidelberg (2007)
18. Prajna, S., Jadbabaie, A.: Safety verification of hybrid systems using barrier certificates. In: Alur, R., Pappas, G.J. (eds.) HSCC 2004. LNCS, vol. 2993, pp. 477-492. Springer, Heidelberg (2004)
19. Sankaranarayanan, S., Sipma, H., Manna, Z.: Scalable analysis of linear systems using mathematical programming. In: Cousot, R. (ed.) VMCAI 2005. LNCS, vol. 3385, pp. 25-41. Springer, Heidelberg (2005)
20. Sankaranarayanan, S.: Mathematical analysis of programs. Technical report, Standford, PhD thesis (2005)
21. Sankaranarayanan, S., Dang, T., Ivancic, F.: Symbolic Model Checking of Hybrid Systems using Template Polyhedra. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 188-202. Springer, Heidelberg (2008)
22. Seidel, H.-P.: Polar forms and triangular B-spline surfaces. In: Blossoming: The New Polar-Form Approach to Spline Curves and Surfaces, SIGGRAPH 1991 (1991)
23. Tchoupaeva, I.: A symbolic approach to Bernstein expansion for program analysis and optimization. In: Duesterwald, E. (ed.) CC 2004. LNCS, vol. 2985, pp. 120-133. Springer, Heidelberg (2004)
24. Tiwari, A., Khanna, G.: Nonlinear systems: Approximating reach sets. In: Alur, R., Pappas, G.J. (eds.) HSCC 2004. LNCS, vol. 2993, pp. 600-614. Springer, Heidelberg (2004)
25. Vandenberghe, S., Boyd, S.: Semidefinite programming. SIAM Review 38(1), 49-95 (1996)