15.1 Concluding Remarks
In this book, the variance-constrained multi-objective control and filtering problems have been investigated for nonlinear stochastic systems. Latest results on analysis and synthesis problems for nonlinear stochastic systems with multiple performance constraints have been firstly surveyed. Then, in each chapter, for the different kinds of nonlinear stochastic systems, the stability, robustness, and the pre-specified system performance indices, such as system covariance (or variance) constraints, H∞ noise attenuation level, and H2 performance index, are analyzed. Sufficient conditions of robust asymptotically stochastic stability or robust exponential stochastic stability are derived for the closed-loop systems in the presence of the parameter uncertainty, external and internal nonlinear disturbances, sensor and actuator failures, missing measurements, output degradation, etc. Subsequently, the controller/filter synthesis problems are investigated, and sufficient conditions for the existence of the desired controller/filter with which all the pre-specified performance requirements can be simultaneously satisfied are given in terms of feasibility of a set of linear matrix inequalities (LMIs) or Riccati equations.
15.2 Future Research
This book has established a unified theoretical framework for analysis and synthesis of variance-constrained multi-objective control/filtering problems for nonlinear stochastic systems. ...