Abstract
In this paper, we investigate state estimations of a dynamical system in which not only process and measurement noise, but also parameter uncertainties and deterministic input signals are involved. The sensitivity penalization based robust state estimation is extended to uncertain linear systems with deterministic input signals and parametric uncertainties which may nonlinearly affect a state-space plant model. The form of the derived robust estimator is similar to that of the well-known Kalman filter with a comparable computational complexity. Under a few weak assumptions, it is proved that though the derived state estimator is biased, the bound of estimation errors is finite and the covariance matrix of estimation errors is bounded. Numerical simulations show that the obtained robust filter has relatively nice estimation performances.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A. H. Sayed. A framework for state-space estimation with uncertain models. IEEE Transactions on Automatic Control, 2001, 46(7): 998–1013.
T. Zhou. Sensitivity penalization based robust state estimation for uncertain linear systems. IEEE Transactions on Automatic Control, 2010, 55(4): 1018–1024.
T. Kailath, A. H. Sayed, B. Hassibi. Linear Estimation. Upper Saddle River: Prentice Hall, 2000.
C. J. Martin, M. Mintz. Robust filtering and prediction for linear systems with uncertain dynamics: a game-theoretic approach. IEEE Transactions on Automatic Control, 1983, 28(6): 888–896.
A. Garulli, A. Vicino, G. Zappa. Conditional central algorithms for worst case set-membership identificaion and filtering. IEEE Transactions on Automatic Control, 2000, 45(1): 14–23.
C. E. de Souza, U. Shaked. Robust H2 filtering for uncertain systems with measurable inputs. IEEE Transactions on Signal Processing, 1999, 47(8): 2286–2292.
L. Xie, C.E. de Souza, M. Fu. H∞ estimation for discrete-time linear uncertain systems. International Journal of Robust Nonlinear Control, 1991, 1(2): 111–123.
P. Bolzern, P. Colaneri, G. De Nicolao. Guaranteed-cost prediction of discrete — time systems: the finite and infinite-horizon case. IFAC Symposium on Robust Control Design. Budapest: Pergamon, 1997: 471–476.
P. Neveux, E. Blanco, G. Thomas. Robust filtering for linear time invariant continuous systems. IEEE Transactions on Signal Processing, 2007, 55(10): 4752–4757.
T. Zhou. Robust state estimation using error sensitivity penalizing. Proceedings of the 47th IEEE Conference on Decision and Control. Cancun: IEEE, 2008: 2563–2568.
Y. S. Hung, F. Yang. Robust H∞ filtering for discrete time-varying uncertain systems with a known deterministic input. International Journal of Control, 2002, 75(15): 1159–1169.
C. E. de Souza, U. Shaked, M. Fu. Robust H∞ filtering for continuous time varying uncertain systems with deterministic input signals. IEEE Transactions on Signal Processing, 1995, 43(3): 709–719.
J. Qiu, G. Feng, H. Gao. Nonsynchronized state estimation of uncertain discrete-time piecewise affine systems. Journal of Control Theory and Applications, 2010, 8(3): 286–292.
T. Zhou, H. Liang. On asymptotic behaviors of a sensitivity penalization based robust state estimator. Systems & Control Letters, 2011, 60(3): 174–180.
Author information
Authors and Affiliations
Corresponding author
Additional information
This work was supported in part by the 973 Program (Nos. 2009CB320602, 2012CB316504), in part by the National Natural Science Foundation of China (Nos. 61174122, 61021063, 60721003, 60625305), and in part by the Specialized Research Fund for the Doctoral Program of Higher Education, China (No. 20110002110045).
Huabo LIU received his B.Sc. and M.Sc. degrees in Engineering from Chongqing University, China, in 2001 and 2005, respectively. He is a Ph.D. candidate at the Department of Automation, Tsinghua University, and also a lecture at the college of Automation Engineering, Qingdao University, China. His research interest covers robust performance analysis and robust state estimation of multidimensional distributed systems.
Tong ZHOU is currently a professor in the Department of Automation, Tsinghua University. He received his B.Sc. and M.Sc. degrees from University of Electronic Science and Technology of China in 1984 and 1989, respectively, and his Ph.D. degree from Osaka University, Osaka, Japan in 1994. His research interest covers robust control, system identification, signal processing, hybrid systems, communication systems, and their applications to real-world problems.
Rights and permissions
About this article
Cite this article
Liu, H., Zhou, T. Robust state estimation for uncertain linear systems with deterministic input signals. Control Theory Technol. 12, 383–392 (2014). https://doi.org/10.1007/s11768-014-4072-4
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11768-014-4072-4