Analysis Of Fuzzy Stochastic Systems And Control Of Stochastic T-S Fuzzy Systems

Randomness and fuzziness are two different kinds of uncertainty in complex systems. Since their mathematical tools are difficult to fuse, most of the known literature on system analysis and control considers only one of them to modeling the uncertainty, which results in some limitation. This dissertation is meant to combine the theory of stochastic processes and the theory of fuzzy sets to find some new methods of system modeling, analysis and control by describe uncertainty more minutely, and then to balance the optimization and the robustness.If the input or output (observation) variables of a stochastic system are fuzzy, the system becomes a stochastic system on fuzzy number space, and is called a fuzzy stochastic system. The results in the dissertation cover various aspects of fuzzy stochastic systems, including the following: The notions of covariance and cross-covariance are introduced. The mean-square (m.s.) convergences of the sequence of fuzzy random variables are discussed, and then some theorems on m.s. fuzzy stochastic analysis and stationary fuzzy stochastic processes are proved. The equations of the mean value functions and the covariance functions are established for dynamical systems whose inputs are fuzzy stochastic processes. An existence and uniqueness theorem of Ito fuzzy stochastic differential equations is proved, some explicit representations of solutions and the equations of statistical characteristics are deduced for linear fuzzy stochastic differential equations, and numericalmethods to nonlinear fuzzy stochastic differential equations are proposed, The conditions for stability and observability of fuzzy linear systems are derived. The Kalman filter algorithms of linear fuzzy stochastic systems are brought forward. Moreover, the statistical linear regression with fuzzy observation data is discussed.When the parameters of a Tagaki-Sugeno(T-S) fuzzy system are perturbed with random noise, the system turns to be a stochastic T-S system. Essentially, it is a nonlinear stochastic differential system. The second part ofthe dissertation focuses on the stability analysis and control of the stochastic T-S systems. The main contributions include: The conditions of global m.s.exponential stability, global almost surely (a,s.) exponential stability andglobal robust exponential stability are constructed. A set of linear matrix inequality (LMI) conditions is proposed to guarantee the clossd-loop m.s. (energy) stability and a.s. (path) stability. Performance-oriented controller synthesis is also discussed and muti-objective controller can be designed based on it. LMI design methods for robust controller ,H controller and robust H, controller of the stochastic T-S systems with unmodeling uncertainties are introduced. Finally, various controllers developed in this dissertation are applied to Lorenz chaos system with random perturbations, and compared with traditional controllers. All me analysis and controller designs are based on LMIs, that are facile to be solved by Matlab software...