Interval methods for simulation of dynamical systems with state-dependent switching characteristics

Proceedings of the IEEE International Conference on Control Applications

Volumn , Issue , 2007, Pages 355-360

  Rauh, Andreas ^a,b   Kletting, Marco ^a   Aschemann, Harald ^a   Hofer, Eberhard P ^a  

^a IEEE

^b UNIVERSITY OF ULM   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

DYNAMICAL MODELS; STATE VARIABLES;

ALGORITHMS; COMPUTER SIMULATION; DIGITAL ARITHMETIC; PARAMETER ESTIMATION; SWITCHING SYSTEMS;

DYNAMICAL SYSTEMS;

EID: 43049163968     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/CCA.2006.285918     Document Type: Conference Paper

References (16)

1. C. Canudas de Wit, H. Olsson, K. J. Åström, and P. Lischinsky, "A New Model for Control of Systems with Friction," IEEE Transactions on Automatic Control, vol. 40, pp. 419-425, 1995.
2. L. F. Shampine and S. Thompson, "Event Location for Ordinary Differential Equations," Computers and Mathematics with Applications. vol. 39, pp. 43-54, 2000.
3. C. Moler, Numerical Computing with MATLAB. SIAM, 2004.
4. L. Jaulin, M. Kieffer, O. Didrit, and É. Walter, "Guaranteed Recursive Nonlinear State Bounding using Interval Analysis," International Journal of adaptive, control and signal processing, vol. 16, pp. 193-218, 2002.
5. N. S. Nedialkov and M. v. Mohrensehildt, "Rigorous Simulation of Hybrid Dynamic Systems with Symbolic and Interval Methods," in Proc. of American Control Conference ACC, Anchorage, USA, 2002. pp. 140-147.
6. M. Wisse, A. L. Schwab, and R. Q. vd. Linde, "A 3D Passive Dynamic Biped with Yaw and Roll Compensation," Robotica, vol. 19, pp. 275-284, 2001.
7. F. Pfeiffer and C. Glocker, Multibody Dynamics with Unilateral Contacts. Wiley Series in Nonlinear Science, John Wiley & Sons Inc., 1996.
8. H. K. Khalil, Nonlinear Systems, 3rd ed. Prentice Hall, 2002.
9. N. S. Nedialkov, "Computing Rigorous Bounds on the Solution of an Initial Value Problem for an Ordinary Differential Equation," Ph.D. dissertation, Graduate Department of Computer Science, University of Toronto, 1999.
10. L. Jaulin, M. Kieffer, O. Didrit, and É. Walter, Applied Interval Analysis. London: Springer, 2001.
11. R. Moore, Methods and Applications of Interval Analysis. Philadelphia: SIAM, 1979.
12. A. Rauh, M. Kletting, H. Aschemann, and E. P. Hofer, "Application of Interval Arithmetic Simulation Techniques to Wastewater Treatment Processes," in Proc. of MIC 2004, Grindelwald, Switzerland, 2004, pp. 287-293.
13. M. Berz and K. Makino, "Verified Integration of ODEs and Flows Using Differential Algebraic Methods on High-Order Taylor Models," Reliable Computing, vol. 4, pp. 361-369, 1998.
14. M. Kletting, A. Rauh, H. Aschemann, and E. P. Hofer, "Consistency Techniques for Simulation of Wastewater Treatment Processes with Uncertainties," in DVD Proc. of IFAC World. Congress 2005, Prague, Czech Republic, 2005.
15. R. Rihm, "Über Einschließungsverfahren für gewöhnliche Anfangswertprobleme und ihre Anwendung auf Differentialgleichungen mit unstetiger rechter Seite," Ph.D. dissertation, University of Karlsruhe, Germany, 1993, (in German).
16. A. Rauh and E. P. Hofer, "Interval Arithmetic Optimization Techniques for Uncertain Discrete-Time Systems," in Proc. of 13th Int. Workshop on Dynamics and Control, Wiesensteig, Germany, 2005, pp. 141-148.