Multiobjective Optimization Analysis And Control For Nonlinear Stochastic Systems

In recent years,the hybridH₂/H_∞control has been widely concerned by scholars,and some research results have been achieved.Based on the previous studies,this paper studies nonlinear stochastic systems with multiobjective control problems based on T-S model.The detailed contents are as follows:1.For a class of nonlinear stochastic time-delay financial systems,the design problem of multiobjectiveH₂/H_∞time delay state feedback controller is studied.Firstly,the T-S model with parameter uncertainty is used to effectively approximate nonlinear stochastic time delay systems and give fuzzy delay feedback control.Secondly,the multiobjective H₂/H_∞fuzzy control problem for nonlinear stochastic time-delay financial systems is transformed into a linear matrix inequality（LMIs）-constrained multiobjective optimization problem（MOP）,and then the LMIs-constrained multiobjective evolutionary algorithm（MOEA）is used to find the Pareto optimality of MOP.Finally,a financial system example is given to verify the effectiveness of the method.2.For a class of nonlinear stochastic hybrid time-delay financial systems,the design problem of multiobjectiveH₂/H_∞non-fragile controllers is studied.Firstly,the T-S model is used to effectively approximate nonlinear stochastic time-delay systems and two expressions of fuzzy non-fragile controllers are given.Secondly,two types of multiobjectiveH₂/H_∞non-fragile control problems for nonlinear stochastic mixed time-delay financial systems are transformed into LMIs-constrained MOP,respectively.Then the Pareto optimal solution of MOP can be obtained by means of LMIs-constrained MOEA,and finally a financial system example is given to verify the validity of the method.3.For a class of nonlinear stochastic systems,the design of the multiobjective H₂/H_∞state feedback controller is studied based on event-triggered conditions.Firstly,the T-S model is used to approximate the nonlinear stochastic time-delay system effectively and the event-triggered conditions under non-uniform sampling are given.On this basis,the MOP of nonlinear stochastic system is transformed into LMIs-constrained MOP,and then the Pareto optimal solution of MOP is solved by LMIs-constrained MOEA.Finally,the effectiveness of the results is verified by numerical simulation.