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Kernel characterization of an interval function. (English) Zbl 1302.65117
Summary: This paper proposes a set-membership approach to characterize the kernel of an interval-valued function. In the context of a bounded-error estimation, this formulation makes it possible to embed all uncertainties of the problem inside the interval function and thus to avoid bisections with respect to all these uncertainties. To illustrate the principle of the approach, two testcases taken from robotics will be presented. The first testcase deals with the characterization of all loops of a mobile robot from proprioceptive measurements only. The second testcase is the localization of a robot from range-only measurements.

65G20 Algorithms with automatic result verification
65G30 Interval and finite arithmetic
65G40 General methods in interval analysis
68T40 Artificial intelligence for robotics
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[1] Aubry, C.; Desmare, R.; Jaulin, L., Loop detection of mobile robots using interval analysis, Automatica, 49, 463-470, (2013) · Zbl 1259.93078
[2] Braems, I.; Berthier, F.; Jaulin, L.; Kieffer, M.; Walter, E., Guaranteed estimation of electrochemical parameters by set inversion using interval analysis, J. Electroanal. Chem., 495, 1-9, (2001)
[3] Braems, I., Jaulin, L., Kieffer, M., Walter, E.: Guaranteed numerical alternatives to structural identifiability testing. In: In Proceedings of the 40th IEEE Conference on Decision and Control, vol. 4, pp. 3122-3127, Orlando (2001) · Zbl 1020.65029
[4] Brahim-Belhouari, S.; Kieffer, M.; Fleury, G.; Jaulin, L.; Walter, E., Model selection via worst-case criterion for nonlinear bounded-error estimation, IEEE Trans. Instrum. Meas., 49, 653-658, (2000)
[5] Dummit, D.S., Foote, R.M.: Abstract Algebra. Wiley, Hoboken, New Jersey (2004). ISBN: 0-471-43334-9
[6] Goldsztejn, A.: Verified projection of the solution set of parametric real systems. In: Proceedings of the 2nd International Workshop on Global Constrained Optimization and Constraint Satisfaction, Lausanne, Switzerland, 2003 (COCOS 2003), (2003)
[7] Goldsztejn, A., Jaulin, L.: Inner and outer approximations of existentially quantified equality constraints. In Proceedings of the Twelfth International Conference on Principles and Practice of Constraint Programming, (CP 2006), Nantes (France), (2006) · Zbl 1160.68546
[8] Jaulin, L.; Chabert, G., Resolution of nonlinear interval problems using symbolic interval arithmetic, Eng. Appl. Artif. Intell., 23, 1035-1049, (2010)
[9] Jaulin, L., Kieffer, M., Didrit, O., Walter, E.: Applied Interval Analysis, with Examples in Parameter and State Estimation, Robust Control and Robotics. Springer, London (2001) · Zbl 1023.65037
[10] Kreinovich, V.; Lakeyev, A.; Rohn, J.; Kahl, P., Computational complexity and feasibility of data processing and interval computations, Reliab. Comput., 4, 405-409, (1997) · Zbl 0945.68077
[11] LeBars, F.; Sliwka, J.; Reynet, O.; Jaulin, L., State estimation with fleeting data, Automatica, 48, 381-387, (2012) · Zbl 1260.93153
[12] Ramdani, N.; Poignet, P., Robust dynamic experimental identification of robots with set membership uncertainty, IEEE/ASME Trans. Mechatron., 10, 253-256, (2005)
[13] Rauh, A.; Auer, E.; Dotschel, T.; Aschemann, H., Verified stability analysis of continuous-time control systems with bounded parameter uncertainties and stochastic disturbances, Computing, 92, 345-356, (2012) · Zbl 1246.93122
[14] Shary, S., A new technique in systems analysis under interval uncertainty and ambiguity, Reliab. Comput., 8, 321-418, (2002) · Zbl 1020.65029
[15] Walter, E., Pronzato, L.: Identification of Parametric Models from Experimental Data. Springer, London (1997) · Zbl 0864.93014
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