Design And Analysis Of Tracking Control Strategy For Nonlinear Fuzzy Positive Systems

Nonlinear positive systems are common in practical applications,but the inherent property constraints and the complex nature of nonlinearity of positive systems make the analysis and design of such systems still a difficult problem in the control field.Until now,among the many research methods for nonlinear systems,the control method based on Takagi-Sugeno fuzzy model is widely popular.Subsequently,in order to model extremely complex nonlinear systems more accurately and easily,polynomial fuzzy model comes into being.Meanwhile,in order to compromise the problem of system uncertainty,the interval type-2 fuzzy logic is proposed which includes uncertainty directly into membership function.Compared with system stability,tracking control research is more challenging.In this dissertation,the tracking control design for nonlinear fuzzy positive system is studied.Factors that may exist in the actual system,such as time-delay,parameter uncertainties,external disturbances,restricted network bandwidth resources and system state unutilizable,are considered comprehensively,under these factors,the problems of fuzzy tracking controller design and system stability analysis are studied,and the purpose of reducing the tracking error is achieved.The main work of this dissertation is summarized as follows:First,for the T-S fuzzy positive system tracking control problem,the T-S fuzzy tracking controller is designed by using the imperfect premise matching of membership function technique.For all the positive and basic stability non-convex conditions generated during the analysis,they are solved by designing a convexification scheme based on matrix transformation technique,thus,the optimal numerical solution of the gain matrix in the fuzzy tracking controller is found.Finally,the effectiveness of the designed controller in the T-S fuzzy positive system tracking control strategy is verified using simulation examples.Second,for the fuzzy positive system tracking control problem with time-varying delay,the state feedback T-S fuzzy tracking controller is designed.All the non-convex problems in the positive conditions and stability conditions,as well as the non-convex terms caused by the time delay of the system,are solved by using the proposed convexification scheme based on matrix decoupling and transformation techniques.Moreover,in order to reduce the conservatism of the basic stability analysis conditions,an improved Taylor-Series Membership Functions dependence method is proposed,which leads to a further relaxed stability analysis condition.Finally,the simulation example demonstrates that the proposed membership function dependence method can effectively reduce the tracking error.Third,for the problem of tracking control of fuzzy positive systems with parameter uncertainty and external disturbances,a state feedback T-S fuzzy tracking controller is designed based on the interval type-2 fuzzy sets.To address the problem of strong conservativeness of the stability conditions caused by the missing information of the membership function in the basic analysis conditions,an improved interval type-2Piecewise-Linear Membership Functions dependence method is proposed,which relaxes the basic stability analysis conditions by introducing the upper and lower boundary information of the membership function,the approximation error information and the state boundary information into the basic stability analysis conditions.Moreover,the method allows the users to freely choose the reference embedded type-1 membership function to be utilized,avoiding the tedious optimization search process.Finally,the effectiveness of the proposed method in reducing tracking errors is verified by simulation examples.Forth,for the problem of fuzzy positive system tracking control under the bandwidth resources limitation of network system and uncertainty of system parameters,an event-triggered tracking controller design method based on interval type-2 fuzzy set is proposed,and a polynomial dynamic event triggering mechanism is given,which improves the flexibility of event-triggered control design and reduces the network resource overhead.For the problem of premise variable mismatch between fuzzy model and fuzzy controller,a linear constrained recursive estimation algorithm between two sets of premise variables is given,thus solving the premise variable mismatch problem.In addition,using the boundary values of the approximation errors in each suboperating domain,an improved interval type-2 membership function dependence method is proposed to relax the basic analysis condition of missing membership function information.Finally,the effectiveness of the proposed method in reducing tracking errors and saving network resources is verified by simulation examples.At last,for the polynomial fuzzy positive system tracking control problem in which the system state is not fully measurable,a static output feedback polynomial fuzzy tracking controller is designed.In the design process,due to the introduction of output matrix,when the positive condition and stability condition need to be solved numerically,the new form of non-convex conditions are obtained.In order to transform the non-convex conditions into the solvable convex conditions,a new scalar interpolation conversion method is proposed.To address the problem of strong conservativeness of the basic analysis conditions under the independent membership function technique,a improved polynomial membership function dependence method is used to introduce the nature of the membership function,the membership function boundary information and the output state boundary information into the basic stability analysis conditions,thus reducing the conservativeness of the tracking controller design caused by the missing affiliation function information.Finally,the effectiveness of the proposed method in the design process of polynomial fuzzy positive system tracking control strategy is verified by simulation examples.