Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 416358, 15 pages
http://dx.doi.org/10.1155/2012/416358
Review Article

A Review on Analysis and Synthesis of Nonlinear Stochastic Systems with Randomly Occurring Incomplete Information

Hongli Dong,1,2 Zidong Wang,3,4 Xuemin Chen,5 and Huijun Gao6

1College of Electrical and Information Engineering, Northeast Petroleum University, Daqing 163318, China
2Institute for Automatic Control and Complex Systems, University of Duisburg-Essen 47057, Germany
3Department of Automation, Tsinghua University, Beijing 100084, China
4Department of Information Systems and Computing, Brunel University, Uxbridge, Middlesex, UB8 3PH, UK
5Department of Engineering Technology, Texas Southern University, 3100 Cleburne Street, Houston, TX 77004, USA
6Research Institute of Intelligent Control and Systems, Harbin Institute of Technology, Harbin 150001, China

Received 11 November 2012; Accepted 21 November 2012

Academic Editor: Bo Shen

Copyright © 2012 Hongli Dong et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In the context of systems and control, incomplete information refers to a dynamical system in which knowledge about the system states is limited due to the difficulties in modeling complexity in a quantitative way. The well-known types of incomplete information include parameter uncertainties and norm-bounded nonlinearities. Recently, in response to the development of network technologies, the phenomenon of randomly occurring incomplete information has become more and more prevalent. Such a phenomenon typically appears in a networked environment. Examples include, but are not limited to, randomly occurring uncertainties, randomly occurring nonlinearities, randomly occurring saturation, randomly missing measurements and randomly occurring quantization. Randomly occurring incomplete information, if not properly handled, would seriously deteriorate the performance of a control system. In this paper, we aim to survey some recent advances on the analysis and synthesis problems for nonlinear stochastic systems with randomly occurring incomplete information. The developments of the filtering, control and fault detection problems are systematically reviewed. Latest results on analysis and synthesis of nonlinear stochastic systems are discussed in great detail. In addition, various distributed filtering technologies over sensor networks are highlighted. Finally, some concluding remarks are given and some possible future research directions are pointed out.