Quantified Set Inversion Algorithm with Applications to Control
- 32 Downloads
In this paper, a new algorithm based on Set Inversion techniques and Modal Interval Analysis is presented. This algorithm allows one to solve problems involving quantified constraints over the reals through the characterization of their solution sets. The presented methodology can be applied to a wide range of problems involving uncertain (non)linear systems. Finally, an advanced application is solved.
KeywordsMathematical Modeling Linear System Computational Mathematic Industrial Mathematic Interval Analysis
Unable to display preview. Download preview PDF.
- 2.Benhamou, F. and Goulard, F.: Universally Quantified Interval Constraints, Lecture Notes in Computer Science 5 (4) (2000).Google Scholar
- 4.Brown, C. W.: Quantifier Elimination by Partial Cylindrical Algebraic Decomposition, http://www.cs.usna.edu/~qepcad/B/QEPCAD.html.
- 5.Chauvin, C., Muller, M., and Weber, A.: An Application of Quantifier Elimination to Mathematical Biology, in: Computer Algebra in Science and Engineering, World Scientific, 1994, pp. 287–296.Google Scholar
- 6.Collins, G. E.: Quantifier Elimination for Real Closed Fields by Cylindrical Algebraic Decomposition, in: 2nd GI Conf. Automata Theory and Formal Languages, Vol. 33, Springer, 1975, pp. 134–189.Google Scholar
- 9.Gardeñes, E., Trepat, A., and Janer, J.: Sigla-PL/1: Development and Applications, in: Nickel, K. L. E. (ed.), Interval Mathematics 80, Springer, 1980, pp. 301–315.Google Scholar
- 10.Garloff, J. and Graf, B.: Solving Strict Polynomial Inequalities by Bernstein Expansion, in: The Use of Symbolic Methods in Control System Analysis and Design, 1999, pp. 339–352.Google Scholar
- 11.Hong, H.: Simple Solution Formula Construction in Cylindrical Algebraic Decomposition Based Quantifier Elimination, in: Proc. ISSAC’92, International Symposium on Symbolic and Algebraic Computation, 1992, pp. 177–188.Google Scholar
- 12.Ioakimidis, N. I.: REDLOG-Aided Derivation of Feasibility Conditions in Applied Mechanics and Engineering Problems under Simple Inequality Constraints, Journal of Mechanical Engineering (Strojnícky Casopis) 50 (1) (1999), pp. 58–69.Google Scholar
- 16.Ratschan, S.: Solving Existentially Quantified Constraints with One Equality and Arbitrarily Many Inequalities, in: Rossi, F. (ed.), Proceedings of the Ninth International Conference on Principles and Practice of Constraint Programming, Springer, 2003, pp. 615–633.Google Scholar
- 17.Ratschan, S. and Vehí, J.: Robust Pole Clustering of Parametric Uncertain Systems Using Interval Methods, in: Colaneri, P. (ed.), Robust Control Design 2003-Proceedings of the 4th IFAC Symposium, Elsevier Science, 2004.Google Scholar
- 19.Stevens, B. and Lewis, F.: Aircraft Control and Simulation, Wiley, 1993.Google Scholar