[
Becis-Aubry, Y. (2020). Ellipsoidal constrained state estimation in presence of bounded disturbances, Preprint, arxiv.org/pdf/2012.03267v1.pdf.
]Search in Google Scholar
[
Bünger, F. (2020). A Taylor model toolbox for solving ODEs implemented in MATLAB/INTLAB, Journal of Computational and Applied Mathematics 368: 112511.10.1016/j.cam.2019.112511
]Search in Google Scholar
[
Bouissou, O., Chapoutot, A. and Djoudi, A. (2013). Enclosing temporal evolution of dynamical systems using numerical methods, in G. Brat et al. (Eds), NASA Formal Methods, Springer-Verlag, Berlin/Heidelberg, pp. 108–123.10.1007/978-3-642-38088-4_8
]Search in Google Scholar
[
Bourgois, A. and Jaulin, L. (2021). Interval centred form for proving stability of non-linear discrete-time systems, in T. Dang and S. Ratschan (Eds), Symbolic-Numeric Methods for Reasoning About CPS and IoT, Open Publishing Association, Den Haag, pp. 1–17.10.4204/EPTCS.331.1
]Search in Google Scholar
[
Chapoutot, A. (2010). Interval slopes as a numerical abstract domain for floating-point variables, in R. Cousot and M. Martel (Eds), Static Analysis. SAS 2010, Lecture Notes in Computer Science, Vol. 6337, Springer, Berlin/Heidelberg, pp. 184–200.10.1007/978-3-642-15769-1_12
]Search in Google Scholar
[
Chen, M. and Rincon-Mora, G. (2006). Accurate electrical battery model capable of predicting runtime and I-V performance, IEEE Transactions on Energy Conversion 21(2): 504–511.10.1109/TEC.2006.874229
]Search in Google Scholar
[
Cornelius, H. and Lohner, R. (1984). Computing the range of values of real functions with accuracy higher than second order, Computing 33(3–4): 331–347.10.1007/BF02242276
]Search in Google Scholar
[
de Berg, M., Cheong, O., van Kreveld, M. and Overmars, M. (2008). Computational Geometry: Algorithms and Applications, 3rd Edn, Springer, Berlin/Heidelberg.10.1007/978-3-540-77974-2
]Search in Google Scholar
[
Erdinc, O., Vural, B. and Uzunoglu, M. (2009). A dynamic Lithium-ion battery model considering the effects of temperature and capacity fading, International Conference on Clean Electrical Power, Capri, Italy, pp. 383–386.
]Search in Google Scholar
[
Černý, M. (2012). Goffin’s algorithm for zonotopes, Kybernetika 48(5): 890–906.
]Search in Google Scholar
[
Farrera, B., López-Estrada, F.-R., Chadli, M., Valencia-Palomo, G. and Gómez-Peñate, S. (2020). Distributed fault estimation of multi-agent systems using a proportional-integral observer: A leader-following application, International Journal of Applied Mathematics and Computer Science 30(3): 551–560, DOI: 10.34768/amcs-2020-0040.
]Search in Google Scholar
[
Goubault, E., Mullier, O., Putot, S. and Kieffer, M. (2014). Inner approximated reachability analysis, 17th International Conference on Hybrid Systems: Computation and Control, Berlin, Germany, pp. 163–172.
]Search in Google Scholar
[
Griewank, A. (2000). Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation, SIAM, Philadelphia.
]Search in Google Scholar
[
Hairer, E., Lubich, C. and Wanner, G. (2002). Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations, Springer, Berlin/Heidelberg.10.1007/978-3-662-05018-7
]Search in Google Scholar
[
Halder, A. (2018). On the parameterized computation of minimum volume outer ellipsoid of Minkowski sum of ellipsoids, IEEE Conference on Decision and Control (CDC), Miami Beach, USA, pp. 4040–4045.
]Search in Google Scholar
[
Hanebeck, U.D., Briechle, K. and Rauh, A. (2003). Progressive Bayes: A new framework for nonlinear state estimation, in B.V. Dasarathy (Ed.), Multisensor, Multisource Information Fusion: Architectures, Algorithms, and Applications 2003, International Society for Optics and Photonics, Bellingham, pp. 256–267.10.1117/12.487806
]Search in Google Scholar
[
Hoefkens, J. (2001). Rigorous Numerical Analysis with High-Order Taylor Models, PhD thesis, Michigan State University, East Lansing, https://groups.nscl.msu.edu/nscl_library/Thesis/Hoefkens,%20Jens.pdf.
]Search in Google Scholar
[
Houska, B., Villanueva, M. and Chachuat, B. (2015). Stable set-valued integration of nonlinear dynamic systems using affine set-parameterizations, SIAM Journal on Numerical Analysis 53(5): 2307–2328.10.1137/140976807
]Search in Google Scholar
[
Jambawalikar, S. and Kumar, P. (2008). A note on approximate minimum volume enclosing ellipsoid of ellipsoids, International Conference on Computational Sciences and Its Applications, Perugia, Italy, pp. 478–487.
]Search in Google Scholar
[
Jaulin, L., Kieffer, M., Didrit, O. and Walter, É. (2001). Applied Interval Analysis, Springer-Verlag, London.10.1007/978-1-4471-0249-6
]Search in Google Scholar
[
John, F. (1948). Extremum problems with inequalities as subsidiary conditions, Studies and Essays Presented to R. Courant on his 60th Birthday, Interscience Publishers, New York, pp. 187–204.
]Search in Google Scholar
[
Julier, S., Uhlmann, J. and Durrant-Whyte, H. (2000). A new approach for the nonlinear transformation of means and covariances in filters and estimators, IEEE Transactions on Automatic Control 45(3): 477–482.10.1109/9.847726
]Search in Google Scholar
[
Kalman, R. (1960). A new approach to linear filtering and prediction problems, Transaction of the ASME: Journal of Basic Engineering 82(Series D): 35–45.10.1115/1.3662552
]Search in Google Scholar
[
Krasnochtanova, I., Rauh, A., Kletting, M., Aschemann, H., Hofer, E.P. and Schoop, K.-M. (2010). Interval methods as a simulation tool for the dynamics of biological wastewater treatment processes with parameter uncertainties, Applied Mathematical Modeling 34(3): 744–762.10.1016/j.apm.2009.06.019
]Search in Google Scholar
[
Krishnaswami, G. and Senapati, H. (2019). An introduction to the classical three-body problem: From periodic solutions to instabilities and chaos, Reson 24: 87–114, DOI: 10.1007/s12045-019-0760-1.10.1007/s12045-019-0760-1
]Search in Google Scholar
[
Kühn, W. (1999). Rigorous error bounds for the initial value problem based on defect estimation, Technical report, http://www.decatur.de/personal/papers/defect.zip.
]Search in Google Scholar
[
Kurzhanskii, A.B. and Vályi, I. (1997). Ellipsoidal Calculus for Estimation and Control, Birkhäuser, Boston.10.1007/978-1-4612-0277-6
]Search in Google Scholar
[
Kurzhanskiy, A. and Varaiya, P. (2006). Ellipsoidal Toolbox (ET), Proceedings of the 45th IEEE Conference on Decision and Control, San Diego, USA, pp. 1498–1503.
]Search in Google Scholar
[
Makino, K. and Berz, M. (2004). Suppression of the wrapping effect by Taylor model-based validated integrators, Technical Report MSU HEP 40910, Michigan State University, East Lansing.
]Search in Google Scholar
[
Mayer, G. (2017). Interval Analysis and Automatic Result Verification, De Gruyter, Berlin/Boston.10.1515/9783110499469
]Search in Google Scholar
[
Mejdi, S., Messaoud, A. and Ben Abdennour, R. (2020). Fault tolerant multicontrollers for nonlinear systems: A real validation on a chemical process, International Journal of Applied Mathematics and Computer Science 30(1): 61–74, DOI: 10.34768/amcs-2020-0005.
]Search in Google Scholar
[
Moore, R. (1966). Interval Arithmetic, Prentice-Hall, Englewood Cliffs.
]Search in Google Scholar
[
Moore, R., Kearfott, R. and Cloud, M. (2009). Introduction to Interval Analysis, SIAM, Philadelphia.10.1137/1.9780898717716
]Search in Google Scholar
[
Musielak, Z.E. and Quarles, B. (2014). The three-body problem, Reports on Progress in Physics 77(6): 065901.10.1088/0034-4885/77/6/06590124913140
]Search in Google Scholar
[
Neumaier, A., Fuchs, M., Dolejsi, E., Csendes, T., Dombi, J. and Banhelyi, B. (2007). Application of clouds for modeling uncertainties in robust space system design, Technical Report 05-5201, European Space Agency, Paris, http://www.esa.int/gsp/ACT/doc/ARI/ARI%20Study%20Report/ACT-RPT-INF-ARI-055201-Clouds.pdf.
]Search in Google Scholar
[
Papoulis, A. (1965). Probability, Random Variables, and Stochastic Processes, McGraw-Hill, Tokyo.
]Search in Google Scholar
[
Rauh, A., Bourgois, A. and Jaulin, L. (2021a). Ellipsoidal enclosure techniques for a verified simulation of initial value problems for ordinary differential equations, 5th International Conference on Control, Automation and Diagnosis (ICCAD’21), Grenoble, France, (accepted for publication).10.1109/ICCAD52417.2021.9638755
]Search in Google Scholar
[
Rauh, A., Bourgois, A. and Jaulin, L. (2021b). Union and intersection operators for thick ellipsoid state enclosures: Application to bounded-error discrete-time state observer design, Algorithms 14(3): 88.10.3390/a14030088
]Search in Google Scholar
[
Rauh, A., Briechle, K. and Hanebeck, U.D. (2009). Nonlinear measurement update and prediction: Prior density splitting mixture estimator, IEEE International Conference on Control Applications CCA 2009, St. Petersburg, Russia, pp. 1421–1426.
]Search in Google Scholar
[
Rauh, A., Butt, S.S. and Aschemann, H. (2013). Nonlinear state observers and extended Kalman filters for battery systems, International Journal of Applied Mathematics and Computer Science 23(3): 539–556, DOI: 10.2478/amcs-2013-0041.10.2478/amcs-2013-0041
]Search in Google Scholar
[
Rauh, A. and Jaulin, L. (2021). A novel thick ellipsoid approach for verified outer and inner state enclosures of discrete-time dynamic systems, 19th IFAC Symposium on System Identification: Learning Models for Decision and Control, online.10.1016/j.ifacol.2021.08.426
]Search in Google Scholar
[
Rauh, A., Kletting, M., Aschemann, H. and Hofer, E.P. (2007). 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.2005.07.029
]Search in Google Scholar
[
Rauh, A., Weitschat, R. and Aschemann, H. (2010). Modellgestützter Beobachterentwurf zur Betriebszustands- und Alterungserkennung für Lithium-Ionen-Batterien, VDI-Berichte 2105: Innovative Fahrzeugantriebe 2010 Die Vielfalt der Mobilität: Vom Verbrenner bis zum E-Motor: 7. VDI-Tagung Innovative Fahrzeugantriebe, Dresden, Germany, pp. 377–382.
]Search in Google Scholar
[
Reuter, J., Mank, E., Aschemann, H. and Rauh, A. (2016). Battery state observation and condition monitoring using online minimization, 21st Internatioanl Conference on Methods and Models in Automation and Robotics, Międzyzdroje, Poland, pp. 1223–1228.
]Search in Google Scholar
[
Romig, S., Jaulin, L. and Rauh, A. (2019). Using interval analysis to compute the invariant set of a nonlinear closed-loop control system, Algorithms 12(12): 262.10.3390/a12120262
]Search in Google Scholar
[
Stengel, R. (1994). Optimal Control and Estimation, Dover Publications, New York.
]Search in Google Scholar
[
Tarbouriech, S., Garcia, G., Gomes da Silva, J. and Queinnec, I. (2011). Stability and Stabilization of Linear Systems With Saturating Actuators, Springer-Verlag, London.10.1007/978-0-85729-941-3
]Search in Google Scholar
[
Tóth, B. and Csendes, T. (2005). Empirical investigation of the convergence speed of inclusion functions in a global optimization context, Reliable Computing 11: 253–273.10.1007/s11155-005-6890-z
]Search in Google Scholar
[
Villanueva, M., Houska, B. and Chachuat, B. (2015). Unified framework for the propagation of continuous-time enclosures for parametric nonlinear ODEs, Journal of Global Optimization 62(3): 575–613.10.1007/s10898-014-0235-6
]Search in Google Scholar
[
Wang, B., Shi, W. and Miao, Z. (2015). Confidence analysis of standard deviational ellipse and its extension into higher dimensional Euclidean space, PLOS ONE 10(3): 1–17.10.1371/journal.pone.0118537435897725769048
]Search in Google Scholar
[
Yildirim, E.A. (2006). On the minimum volume covering ellipsoid of ellipsoids, SIAM Journal on Optimization 17(3): 621–641.10.1137/050622560
]Search in Google Scholar
