Variance-Constrained Multi-Objective Stochastic Control and Filtering

Chapter 8Variance-Constrained H_∞ Control with Multiplicative Noises

Among many practical systems, plants may be modeled by bilinear systems (which are also known as systems with multiplicative noises) since some characteristics of nonlinear systems can be closely approximated by bilinear models rather than linearized models. The bilinear system is a kind of “nearly linear” yet nonlinear system. The related problems of bilinear systems, such as the state analysis and the parameter estimation, are much more difficult to solve than those of the linear systems. Up to now, it has been known that bilinear systems could describe many real processes in the fields of socioeconomics, ecology, agriculture, biology, and industry, etc. In particular, bilinear models are widely used to model nonlinear processes in signal and image processing, as well as communication systems analysis, such as channel equalization, echo cancelation, nonlinear tracking, electroencephalogram (EEG) signal classification, multiplicative disturbance tracking, to name but a few key ones. As a result, control problems have been extensively studied for bilinear systems and many research results have been reported in the literature. However, unfortunately, up to now, the multi-objective control problems that take multiple performance requirements, including variance constraints, H_∞ specifications, and other performances, have received little attention for stochastic systems with multiplicative noises, and remain open ...