A distributed Kalman filter with symbolic zonotopes and unique symbols provider for robust state estimation in CPS

References

• Alamo, T., Bravo, J. M., & Camacho, E. F. (2005). Guaranteed state estimation by zonotopes. Automatica, 41(6), 1035–1043. doi: 10.1016/j.automatica.2004.12.008
   Web of Science ®Google Scholar
• Battistelli, G., & Chisci, L. (2016). Stability of consensus extended Kalman filter for distributed state estimation. Automatica, 68, 169–178. doi: 10.1016/j.automatica.2016.01.071
   Web of Science ®Google Scholar
• Benavoli, A., & Piga, D. (2016). A probabilistic interpretation of set-membership filtering: Application to polynomial systems through polytopic bounding. Automatica, 70, 158–172. doi: 10.1016/j.automatica.2016.03.021
   Web of Science ®Google Scholar
• Cattivelli, F. S., & Sayed, A. H. (2010). Diffusion strategies for distributed Kalman filtering and smoothing. IEEE Transactions on Automatic Control, 55(9), 2069–2084. doi: 10.1109/TAC.2010.2042987
   Web of Science ®Google Scholar
• Combastel, C. (2015a). Merging Kalman filtering and Zonotopic state bounding for robust fault detection under noisy environment. In 9th IFAC safeprocess, and IFAC-PapersOnLine (Vol. 48(21), pp. 289–295).
   Google Scholar
• Combastel, C. (2015b). Zonotopes and Kalman observers: Gain optimality under distinct uncertainty paradigms and robust convergence. Automatica, 55, 265–273. doi: 10.1016/j.automatica.2015.03.008
   Web of Science ®Google Scholar
• Combastel, C. (2016). An extended zonotopic and Gaussian Kalman filter (EZGKF) merging set-membership and stochastic paradigms: Toward non-linear filtering and fault detection. Annual Reviews in Control, 42, 232–243. doi: 10.1016/j.arcontrol.2016.07.002
   Web of Science ®Google Scholar
• Combastel, C (2003). A state bounding observer based on zonotopes. Proc. of European control conf. (ECC).
   Google Scholar
• Combastel, C., & Zolghadri, A (2018). FDI in cyber physical systems: A distributed zonotopic and Gaussian Kalman filter with bit-level reduction. 10th IFAC safeprocess, Warsaw, Poland.
   Google Scholar
• de Figueiredo, L. H., & Stolfi, J. (2004). Affine arithmetic: Concepts and applications. Numerical Algorithms, 37(1-4), 147–158. doi: 10.1023/B:NUMA.0000049462.70970.b6
   Web of Science ®Google Scholar
• del Nozal, A. R., Orihuela, L., & Milláan, P. (2017, July). Distributed consensus-based Kalman filtering considering subspace decomposition. IFAC-PapersOnLine, 50(1), 2494–2499. doi: 10.1016/j.ifacol.2017.08.443
   Google Scholar
• Ferrari, R. M. G., Parisini, T., & Polycarpou, M. M. (2012). Distributed fault detection and isolation of large-scale discrete-time nonlinear systems: An adaptive approximation approach. IEEE Transactions on Automatic Control, 57(2), 275–290. doi: 10.1109/TAC.2011.2164734
   Web of Science ®Google Scholar
• Ge, X., Yang, F., & Han, Q. L. (2017). Distributed networked control systems: A brief overview. Information Sciences, 380, 117–131. doi: 10.1016/j.ins.2015.07.047
   Web of Science ®Google Scholar
• Huang, G., Zomaya, A. Y., Delicato, F. C., & Pires, P. F. (2014). Long term and large scale time synchronization in wireless sensor networks. Computer Communications, 37, 77–91. doi: 10.1016/j.comcom.2013.10.003
   Web of Science ®Google Scholar
• Jaulin, L., Kieffer, M., Didrit, O., & Walter, E. (2001). Applied interval analysis. London: Springer-Verlag. doi:10.1007/978-1-4471-0249-6
   Google Scholar
• Khaitan, S. K., & McCalley, J. D. (2015). Design techniques and applications of cyberphysical systems: A survey. IEEE Systems Journal, 9(2), 350–365. doi: 10.1109/JSYST.2014.2322503
   Web of Science ®Google Scholar
• Khan, U. A., & Moura, J. M. F. (2008). Distributing the Kalman filter for large-scale systems. IEEE Transactions on Signal Processing, 56(10), 4919–4935. doi: 10.1109/TSP.2008.927480
   Web of Science ®Google Scholar
• Kim, T., Shim, H., & Cho, D. D (2016, December). Distributed Luenberger observer design. 2016 IEEE 55th conference on decision and control (CDC). IEEE.
   Google Scholar
• Kühn, W. (1998). Rigorously computed orbits of dynamical systems without the wrapping effect. Computing, 61(1), 47–67. doi: 10.1007/BF02684450
   Web of Science ®Google Scholar
• Kurzhanskiy, A. A., & Varaiya, P. (2007). Ellipsoidal techniques for reachability analysis of discrete-time linear systems. IEEE Transactions on Automatic Control, 52(1), 26–38. doi: 10.1109/TAC.2006.887900
   Web of Science ®Google Scholar
• Le, V. T. H., Stoica, C., Alamo, T., Camacho, E. F., & Dumur, D. (2013). Zonotopic guaranteed state estimation for uncertain systems. Automatica, 49(11), 3418–3424. doi: 10.1016/j.automatica.2013.08.014
   Web of Science ®Google Scholar
• Lee, E. A., & Seshia, S. A. (2017). Introduction to embedded systems: A cyber-physical approach. MIT Press. Retrieved from https://mitpress.mit.edu/books/introduction-embedded-systems-second-edition
   Google Scholar
• Lunze, J. (2014). Control theory of digitally networked dynamic systems. Springer International Publishing. Retrieved from https://www.springer.com/gp/book/9783319011301
   Google Scholar
• Mitra, A., & Sundaram, S. (2018). Distributed observers for LTI systems. IEEE Transactions on Automatic Control, 63(11), 3689–3704. doi: 10.1109/TAC.2018.2798998
   Web of Science ®Google Scholar
• Noack, B., Pfaff, F., & Hanebeck, U (2012). Optimal Kalman gains for combined stochastic and set-membership state estimation. In 51st IEEE conf. on decision and control (CDC) (pp. 4035–4040).
   Google Scholar
• Orihuela, L., Millán, P., Roshany-Yamchi, S., & García, R. A. (2018). Negotiated distributed estimation with guaranteed performance for bandwidth-limited situations. Automatica, 87, 94–102. doi: 10.1016/j.automatica.2017.09.022
   Web of Science ®Google Scholar
• Orihuela, L., Roshany-Yamchi, S., García, R. A.., & Millán, P. (2017). Distributed set-membership observers for interconnected multi-rate systems. Automatica, 85, 221–226. doi: 10.1016/j.automatica.2017.07.041
   Web of Science ®Google Scholar
• Park, S., & Martins, N. C. (2017). Design of distributed LTI observers for state omniscience. IEEE Transactions on Automatic Control, 62(2), 561–576. doi: 10.1109/TAC.2016.2560766
   Web of Science ®Google Scholar
• Puig, V., Saludes, J., & Quevedo, J. (2003). Worst-case simulation of discrete linear time-invariant interval dynamic systems. Reliable Computing, 9, 251–290. doi: 10.1023/A:1024666428387
   Google Scholar
• Raïssi, T., Efimov, D., & Zolghadri, A. (2012). Interval state estimation for a class of nonlinear systems. IEEE Transactions on Automatic Control, 57(1), 260–265. doi: 10.1109/TAC.2011.2164820
   Web of Science ®Google Scholar
• Ramdani, N., Meslem, N., & Candau, Y. (2009). A hybrid bounding method for computing an over-approximation for the reachable set of uncertain nonlinear systems. IEEE Transactions on Automatic Control, 54(10), 2352–2364. doi: 10.1109/TAC.2009.2028974
   Web of Science ®Google Scholar
• Rego, F. F. C., Aguiar, A. P., Pascoal, A. M., & Jones, C. N (2017). A design method for distributed Luenberger observers. 2017 IEEE 56th annual conference on decision and control (CDC). IEEE.
   Google Scholar
• Reppa, V., Polycarpou, M. M., & Panayiotou, C. G (2015). Distributed sensor fault diagnosis for a network of interconnected cyberphysical systems. IEEE Transactions on Control of Network Systems, 2(1), 11–23. doi: 10.1109/TCNS.2014.2367362
   Web of Science ®Google Scholar
• Shen, B., Wang, Z., Hung, Y. S., & Chesi, G. (2011). Distributed H∞ filtering for polynomial nonlinear stochastic systems in sensor networks. IEEE Transactions on Industrial Electronics, 58(5), 1971–1979. doi: 10.1109/TIE.2010.2053339
   Web of Science ®Google Scholar
• Tjarnstrom, F., & Garulli, A (2002). A mixed probabilistic/bounded-error approach to parameter estimation in the presence of amplitude bounded white noise. In 41st IEEE conf. on decision and control (CDC) (Vol. 3, pp. 3422–3427).
   Google Scholar
• Ugrinovskii, V. (2013). Distributed robust estimation over randomly switching networks using H∞ consensus. Automatica, 49(1), 160–168. doi: 10.1016/j.automatica.2012.09.010
   Web of Science ®Google Scholar
• Xiong, J., Jauberthie, C., & Trave-Massuyes, L (2013). Improvements in computational aspects of interval Kalman filtering enhanced by constraint propagation. 11th IEEE int. workshop of ECMSM.
   Google Scholar