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

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.

Stochastic stability and stabilization of a class of piecewise-homogeneous Markov jump linear systems with mixed uncertainties

“…At this case, the precise values of the TRs are not required to be known, but their bounds (upper bounds and lower bounds) are known. Both classes can represent the uncertainty in many physical cases caused by factors like aging of devices and identification errors , and they are widely used in the study of Markovian jump systems. Considerable efforts have been made on the stability , controller design and filtering of MJLSs subject to uncertain TRs.…”

“…Considerable efforts have been made on the stability , controller design and filtering of MJLSs subject to uncertain TRs. Although the aforementioned studies effectively take account of the imperfections of the Markovian structures, they are generally limited to MJLSs with time‐invariant TRs namely time‐homogeneous systems . Their limitations become more highlighted when the uncertainties turn to be very large or fast varying .…”