Quantified set inversion algorithm with applications to control

Reliable Computing

Volumn 11, Issue 5, 2005, Pages 369-382

  Herrero, Pau ^a   Sainz, Miguel A ^a   Veh, Josep ^a   Jaulin, Luc ^b  

^a UNIVERSITY OF GIRONA   (Spain)

^b ENSIETA   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; INVERSE PROBLEMS; NONLINEAR SYSTEMS; PROBLEM SOLVING; REAL TIME SYSTEMS; SET THEORY;

MODAL INTERVAL ANALYSIS; QUANTIFIERS; SET INVERSION TECHNIQUES;

CONTROL SYSTEM ANALYSIS;

EID: 23844468140     PISSN: 13853139     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11155-005-0044-1     Document Type: Conference Paper

References (20)

1. Abdallah, C., Dorato, P., Famularo, D., and Yang, W.: Robust Nonlinear Feedback Design via Quantifier Elimination Theory, International Journal of Robust and Non-Linear Control 9 (1999), pp. 817-822.
2. Benhamou, F. and Goulard, F.: Universally Quantified Interval Constraints, Lecture Notes in Computer Science 5 (4) (2000).
3. Benhamou, F., Goualard, F., Languenou, E., and Christie, M.: Interval Constraint Solving for Camera Control and Motion Planning, ACM Trans. Comput. Logic 5 (4) (2004), pp. 732-767.
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.
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.
7. Dorato., P.: Quantified Multivariate Polynomial Inequalities, IEEE Control Systems Magazine 20 (5) (2000), pp. 48-58.
8. Gardeñes, E., Sainz, M. Á., Jorba, L., Calm, R., Estela, R., Mielgo, H., and Trepat, A.: Modal Intervals, Reliable Computing 7 (2) (2001), pp. 77-111.
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.
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.
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.
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.
13. Jaulin, L., Ratschan, S., and Hardouin, L.: Set Computation for Nonlinear Control, Reliable Computing 10 (1) (2004), pp. 1-26.
14. Jaulin, L. and Walter, E.: Set Inversion via Interval Analysis for Nonlinear Bounded-Error Estimation, Automatica 32 (8) (1993), pp. 1053-1064.
15. Jirstrand, M.: Nonlinear Control System Design by Quantifier Elimination, Journal of Symbolic Computation 24 (2) (1997), pp. 137-152.
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.
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
18. Shary, S. P.: A New Technique in Systems Analysis under Interval Uncertainty and Ambiguity, Reliable Computing 8 (5) (2002), pp. 321-418.
19. Stevens, B. and Lewis, F.: Aircraft Control and Simulation, Wiley, 1993.
20. Sturm, T.: Reasoning over Networks by Symbolic Methods, Applicable Algebra in Engineering Communication and Computing 10 (1) (2000), pp. 79-96.