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Abstract and Applied Analysis
Volume 2013, Article ID 724018, 13 pages
Review Article

Variance-Constrained Multiobjective Control and Filtering for Nonlinear Stochastic Systems: A Survey

1School of Automation, Nanjing University of Science and Technology, Nanjing 210094, China
2School of Information Science and Technology, Donghua University, Shanghai 200051, China
3Department of Information Systems and Computing, Brunel University, Uxbridge, Middlesex UB8 3PH, UK
4Research Institute of Intelligent Control and Systems, Harbin Institute of Technology, Harbin 150001, China
5College of Electrical and Information Engineering, Northeast Petroleum University, Daqing 163318, China
6Shanghai Key Lab of Modern Optical System, Department of Control Science and Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China

Received 2 October 2013; Accepted 6 October 2013

Academic Editor: Bo Shen

Copyright © 2013 Lifeng Ma 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.


The multiobjective control and filtering problems for nonlinear stochastic systems with variance constraints are surveyed. First, the concepts of nonlinear stochastic systems are recalled along with the introduction of some recent advances. Then, the covariance control theory, which serves as a practical method for multi-objective control design as well as a foundation for linear system theory, is reviewed comprehensively. The multiple design requirements frequently applied in engineering practice for the use of evaluating system performances are introduced, including robustness, reliability, and dissipativity. Several design techniques suitable for the multi-objective variance-constrained control and filtering problems for nonlinear stochastic systems are discussed. In particular, as a special case for the multi-objective design problems, the mixed control and filtering problems are reviewed in great detail. Subsequently, some latest results on the variance-constrained multi-objective control and filtering problems for the nonlinear stochastic systems are summarized. Finally, conclusions are drawn, and several possible future research directions are pointed out.