Open Access

Verification Techniques for Sensitivity Analysis and Design of Controllers for Nonlinear Dynamic Systems with Uncertainties

International Journal of Applied Mathematics and Computer Science's Cover Image
International Journal of Applied Mathematics and Computer Science
Verified Methods: Applications in Medicine and Engineering (special issue), Andreas Rauh, Ekaterina Auer, Eberhard P. Hofer and Wolfram Luther (Eds.)

Ackermann, J., Blue, P., Bünte, T., Güvenc, L., Kaesbauer, D., Kordt, M., Muhler, M. and Odenthal, D. (2002). Robust Control: The Parameter Space Approach, 2nd Edn., Springer-Verlag, London.Search in Google Scholar

Aschemann, H., Rauh, A., Kletting, M. and Hofer, E. P. (2006). Flatness-based control of a simplified wastewater treatment plant, Proceedings of the IEEE International Conference on Control Applications CCA 2006, Munich, Germany, pp. 2243-2248.Search in Google Scholar

Auer, E., Rauh, A., Hofer, E. P. and Luther, W. (2008). Validated modeling of mechanical systems with SmartMOBILE: Improvement of performance by ValEncIA-IVP, Proceedings of the Dagstuhl Seminar 06021: Reliable Implementation of Real Number Algorithms. Theory and Practice, Dagstuhl, Germany, Lecture Notes in Computer Science, Vol. 5045, Springer-Verlag, Berlin/Heidelberg, pp. 1-27.Search in Google Scholar

Bendsten, C. and Stauning, O. (2007). FADBAD++, Version 2.1, available at: http://www.fadbad.comSearch in Google Scholar

Bünte, T. (2000). Mapping of Nyquist/Popov theta-stability margins into parameter space, Proceedings of the 3rd IFAC Symposium on Robust Control Design, Prague, Czech Republic.10.1016/S1474-6670(17)36281-XSearch in Google Scholar

Delanoue, N. (2006). Algoritmes numériques pour l'analyse topologique—Analyse par intervalles et théorie des graphes, Ph.D. thesis, École Doctorale d'Angers, Angers, (in French).Search in Google Scholar

Fliess, M., Lévine, J., Martin, P. and Rouchon, P. (1995). Flatness and defect of nonlinear systems: Introductory theory and examples, International Journal of Control 61(6): 1327-1361.10.1080/00207179508921959Search in Google Scholar

Hammersley, J. M. and Handscomb, D. C. (1964). Monte-Carlo Methods, John Wiley & Sons, New York, NY.10.1007/978-94-009-5819-7Search in Google Scholar

Henze, M., Harremoës, P., Arvin, E. and la Cour Jansen, J. (2002). Wastewater Treatment, 3rd Edn., Springer-Verlag, Berlin.Search in Google Scholar

Hermann, R. and Krener, A. J. (1977). Nonlinear controllability and observability, IEEE Transactions on Automatic Control 22(5): 728-740.10.1109/TAC.1977.1101601Search in Google Scholar

Isidori, A. (1989). Nonlinear Control Systems, 2nd Edn., Springer-Verlag, Berlin.Search in Google Scholar

Keil, C. (2007). Profil/BIAS, Version 2.0.4, Available at: www.ti3.tu-harburg.de/keil/profil/Search in Google Scholar

Khalil, H. K. (2002). Nonlinear Systems, 3rd Edn., Prentice-Hall, Upper Saddle River, NJ.Search in Google Scholar

Marquez, H. J. (2003). Nonlinear Control Systems, John Wiley & Sons, Inc., Hoboken, NJ.Search in Google Scholar

Odenthal, D. and Blue, P. (2000). Mapping of frequency response magnitude specifications into parameter space, Proceedings of the 3rd IFAC Symposium on Robust Control Design, Prague, Czech Republic.10.1016/S1474-6670(17)36283-3Search in Google Scholar

Office for Official Publications of the European Communities (2003). Council Directive of 21 May 1991 Concerning Urban Waste Water Treatment (91/271/EEC), Available at: http://ec.europa.eu/environment/water/water-urbanwaste/directiv.htmlSearch in Google Scholar

Rauh, A., Auer, E. and Hofer, E. P. (2007a). ValEncIA-IVP:A comparison with other initial value problem solvers, Proceedings of the 12th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics SCAN 2006, Duisburg, Germany, IEEE Computer Society, Los Alamitos, CA, (on CD-ROM).10.1109/SCAN.2006.47Search in Google Scholar

Rauh, A., Auer, E., Minisini, J. and Hofer, E. P. (2007b). Extensions of ValEncIA-IVP for reduction of overestimation, for simulation of differential algebraic systems, and for dynamical optimization, PAMM 7(1): 1023001-1023002.10.1002/pamm.200700022Search in Google Scholar

Rauh, A., Kletting, M., Aschemann, H. and Hofer, E. P. (2007c). Reduction of overestimation in interval arithmetic simulation of biological wastewater treatment processes, Journal of Computational and Applied Mathematics 199(2): 207-212.10.1016/j.cam.2005.07.029Search in Google Scholar

Rauh, A., Minisini, J. and Hofer, E. P. (2007d). Interval techniques for design of optimal and robust control strategies, Proceedings of the 12th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics SCAN 2006, Duisburg, Germany, IEEE Computer Society, Los Alamitos, CA, (on CD-ROM).10.1109/SCAN.2006.27Search in Google Scholar

Rauh, A. and Hofer, E. P. (2005). Interval arithmetic optimization techniques for uncertain discrete-time systems, Proceedings of the 13th International Workshop on Dynamics and Control, Modeling and Control of Autonomous Decision Support Based Systems, Wiesensteig, Germany, Shaker Verlag, Aachen, pp. 141-148.Search in Google Scholar

Rauh, A. and Hofer, E. P. (2009). Interval methods for optimal control, Proceedings of the 47th Workshop on Variational Analysis and Aerospace Engineering 2007, Erice, Italy, Springer-Verlag, New York, NY, pp. 397-418.Search in Google Scholar

Rauh, A., Minisini, J. and Hofer, E. P. (2009). Towards the development of an interval arithmetic environment for validated computer-aided design and verification of systems in control engineering, Proceedings of the Dagstuhl Seminar 08021: Numerical Validation in Current Hardware Architectures, Dagstuhl, Germany, Lecture Notes in Computer Science, Vol. 5492, Springer-Verlag, Berlin/Heidelberg, pp. 175-188.Search in Google Scholar

Röbenack, K. (2002). On the efficient computation of higher order maps adfkg(x) using Taylor arithmetic and the Campbell-Baker-Hausdorff formula, in A. Zinober and D. Owens (Eds.), Nonlinear and Adaptive Control, Lecture Notes in Control and Information Science, Vol. 281, Springer, Berlin/Heidelberg, pp. 327-336.Search in Google Scholar

Rohn, J. (1994). Positive definiteness and stability of interval matrices, SIAM Journal on Matrix Analysis and Applications 15(1): 175-184.10.1137/S0895479891219216Search in Google Scholar

Rump, S. M. (2007). IntLab, Version 5.4, available at: http://www.ti3.tu-harburg.de/~rump/intlab/Search in Google Scholar

Sienel, W., Bünte, T. and Ackermann, J. (1996). PARADISE—Parametric robust analysis and design interactive software environment: A Matlab-based robust control toolbox, Proceedings of the 1996 IEEE International Symposium on Computer-Aided Control System Design, Dearborn, MI, USA, pp. 380-385.Search in Google Scholar

Sontag, E. D. (1998). Mathematical Control Theory—Deterministic Finite Dimensional Systems, Springer-Verlag, New York, NY.Search in Google Scholar

ISSN:
1641-876X
Language:
English
Publication timeframe:
4 times per year
Journal Subjects:
Mathematics, Applied Mathematics