This paper presents a new improved set-membership algorithm for guaranteed state estimation for non-linear discrete-time systems with an unknown but bounded description of disturbance and noise. In this paper, the non-linear model is linearized first and the difference of convex (DC) programming method is used to outer-bound the linearization error, which is regarded as a disturbance of the system, and the improved set-membership algorithm guaranteed state estimation for the linearization system. An example is given to illustrate the proposed algorithm.
AdjimanCSFloudasCA (1996) Rigorous convex underestimators for general twice-differentiable problems. Journal of Global Optimization9: 23–40.
2.
AlamoTBravoJMCamachoEF (2005) Guaranteed state estimation by zonotopes. Automatica41: 1035–1043.
3.
AlamoTBravoJMRedondoMJ. (2008) A set-membership state estimation algorithm based on DC programming. Automatica44: 216–224.
4.
Ben ChabaneSManiuCSAlamoT. (2014) Improved set-membership estimation approach based on zonotopes and ellipsoids. 2014 European Control Conference (ECC), pp. 993–998.
5.
BlesaJRotondoDPuigV. (2014) FDI and FTC of wind turbines using the interval observer approach and virtual actuators/sensors. Control Engineering Practice24: 138–155.
6.
ChaiWSunXQiaoJ (2011) Brief paper – Improved zonotopic method to set membership identification for systems with time-varying parameters. IET Control Theory & Applications5: 2039–2044.
7.
CombastelC (2005) A state bounding observer for uncertain non-linear continuous-time systems based on zonotopes. 44th IEEE Conference on Decision and Control, 2005 and 2005 European Control Conference, CDC-ECC 05, pp. 7228–7234.
8.
FanCLiHRenX (2015) The order recurrence quantification analysis of the characteristics of two-phase flow pattern based on multi-scale decomposition. Transactions of the Institute of Measurement & Control37: 793–804.
9.
GaoZJiangB (2008) Delay-dependent robust fault detection for a class of nonlinear time-delay systems. 2nd International Symposium on Systems and Control in Aerospace and Astronautics, ISSCAA 2008, pp. 1–6.
10.
GarciaRARaffoGVOrtegaMG. (2015) Guaranteed quadrotor position estimation based on GPS refreshing measurements. IFAC-PapersOnLine48: 67–72.
11.
IngimundarsonABravoJMPuigV. (2009) Robust fault detection using zonotope-based set-membership consistency test. International Journal of Adaptive Control and Signal Processing23: 311–330.
12.
LeVTHAlamoTCamachoEF. (2012) Zonotopic set-membership estimation for interval dynamic systems. American Control Conference (ACC), 2012. 6787–6792.
13.
MaksarovDGNortonJP (2002) Computationally efficient algorithms for state estimation with ellipsoidal approximations. International Journal of Adaptive Control and Signal Processing16: 411–434.
14.
MeseguerJPuigVEscobetT. (2010) Observer gain effect in linear interval observer-based fault detection. Journal of Process Control20: 944–956.
15.
PuigVStancuAEscobetT. (2006) Passive robust fault detection using interval observers: application to the DAMADICS benchmark problem. Control Engineering Practice14: 621–633.
16.
TuyH (1995) DC optimization: theory, methods and algorithms. In: Handbook of Global Optimization. Dordrecht: Kluwer Academic Publishers, pp. 149–216.
17.
WangH-RGaoH-J (2007) robust fault detection for uncertain time-delay systems with Markovian jump parameters. 2007 International Conference on Machine Learning and Cybernetics, pp. 1066–1071.
18.
WuHWangWYeH (2013) Set-membership state estimation with nonlinear equality constraints and quantization. Neurocomputing119: 359–365.
19.
XieLYangH (2013) Interactive parameter estimation for output error moving average systems. Transactions of the Institute of Measurement & Control35: 34–43.
20.
XieXYueDMaT. (2014) Further studies on control synthesis of discrete-time T-S fuzzy systems via augmented multi-indexed matrix approach. IEEE Transactions on Cybernetics44: 2784–2791.
21.
XieXYueDPengC (2016) Multi-instant observer design of discrete-time fuzzy systems: a ranking-based switching approach. IEEE Transactions on Fuzzy Systems, 1–1.
22.
XuL (2014) A proportional differential control method for a time-delay system using the Taylor expansion approximation. Applied Mathematics and Computation236: 391–399.
23.
YangFLiY (2009) Set-membership filtering for discrete-time systems with nonlinear equality constraints. IEEE Transactions on Automatic Control54: 2480–2486.
24.
YiZWangZ (2011) Robust state estimation based on quadratic programming for network packet dropout. 2011 International Conference on Electronics, Communications and Control (ICECC), pp. 1647–1652.
25.
YinSZhuX (2015) Intelligent particle filter and its application to fault detection of nonlinear system. IEEE Transactions on Industrial Electronics62: 3852–3861.
26.
YinSLiuLHouJ (2016a) A multivariate statistical combination forecasting method for product quality evaluation. Information Sciences355–356: 229–236.
27.
YinSWangGGaoH (2016b) Data-driven process monitoring based on modified orthogonal projections to latent structures. IEEE Transactions on Control Systems Technology24: 1480–1487.
28.
YinSZhuXQiuJ. (2016c) State estimation in nonlinear system using sequential evolutionary filter. IEEE Transactions on Industrial Electronics63: 3786–3794.
29.
YouFZhangHWangF (2016) A new set-membership estimation method based on zonotopes and ellipsoids. Transactions of the Institute of Measurement and Control.
30.
ZhouBQianKMaX-D. (2013) A new nonlinear set membership filter based on guaranteed bounding ellipsoid algorithm. Acta Automatica Sinica39: 146–154.
