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

Lifeng Ma,Hongli Dong,Zidong Wang,Guoliang Wei

doi:10.1155/2013/724018

Abstract

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 mixedH2/H∞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.

Highlights

It is widely recognized that, in almost all engineering applications, nonlinearities are inevitable and could not be eliminated thoroughly
We focus mainly on the multiobjective control and filtering problems for nonlinear systems with variance constraints and aim to give a comprehensive survey on some recent advances in this area
It is clear that we cannot expect one particular procedure to apply to all nonlinear systems; quite a lot of tools have been developed to deal with control and filtering problems for nonlinear stochastic systems, including Takagi and Sugeno (T-S) fuzzy model approximation approach, linearization, gain scheduling, sliding mode control, and backstepping, to name but a few key ones

Summary

Introduction

It is widely recognized that, in almost all engineering applications, nonlinearities are inevitable and could not be eliminated thoroughly. Due to the wide appearance of the stochastic phenomena in almost every aspect of our daily life, stochastic systems which have found successful applications in many branches of science and engineering practice have stirred quite a lot of research interests during the past few decades. In addition to the variance constraints, real-world engineering practice desires the simultaneous satisfaction of many other frequently seen performance requirements including stability, robustness, reliability, and energy constraints, to name but a few key ones.

Design techniques

Analysis and Synthesis of Nonlinear Stochastic Systems

Multiobjective Control and Filtering with Variance Constraints

A Special Case of Multiobjective Design

Latest Progress

Conclusions and Future Work