Fuzzy Model-based Gain-scheduling Type Control And State Estimation For Nonlinear Systems

With the rapid development of human production activities,the requirements for automation and control precision in industrial production are increasing.The control objects have also been extended from simple linear systems to complex nonlinear systems,so that the traditional linear control theory can no longer meet the practical needs.Thanks to the famous Takagi-Sugeno（T-S）fuzzy model,nonlinear system control research theory has also made great progress.Since low conservative design conditions allow for a wider range of applications of fuzzy control theory in industrial systems,how to reduce conservatism in the design process has become one of the hot issues in the field in the last decade.In this thesis,the problem of stabilization control and state estimation of nonlinear systems for a class of nonlinear systems based on T-S fuzzy models is specifically investigated for a class of discrete time nonlinear systems.The potential of the gain scheduling method is explored in depth,allowing the controlled system to run different control laws of the design in different subspaces based on the scheduling variables collected in real time,thus allowing for low conservativeness design conditions.The specific research methods,findings and conclusions are summarized below.（1）For a class of discrete-time nonlinear systems based on T-S fuzzy model for the stabilization control problem,the controller structure is enriched by introducing the information of normalized fuzzy weight functions at the current and past moments into the controller.The proposed new fuzzy controller has more switching modes to enhance the stability of the closed-loop system.Specifically,a new switching method is designed to activate online a set of optimal control gain matrices that actually correspond to ech sampling moment.The designed switching law uses only one tuning variable and divides the entire fuzzy space into three independent subintervals,which also helps to reduce the burden of identifying the activation pattern and to find the optimal solution quickly.The simulation results show that the proposed method effectively widens the controllable interval of the controlled system and improves the stability of the closed-loop system of the discrete-time T-S fuzzy system.（2）A novel multi-moment joint switching observer is designed to estimate the state of a nonlinear system based on discrete time T-S fuzzy model for more efficient state estimation of unpredictable system variables.In the design process of the described multi-moment joint switching type observer,the introduction of an exclusive time-varying free matrix corresponding to each switching mode enables the information of the normalized fuzzy weight functions at the current and past moments to be fully utilized and incorporated into the observer gain matrix,effectively reducing the conservativeness of the fuzzy state estimation method.In addition,the proposed scheduling strategy uses only two regulation parameters that take values in a finite set of candidates λ₁ and λ₂,which facilitate the fast search for the optimal multi-moment joint switching type of observer.Finally,two simulation examples are given to verify the effectiveness and advancement of the design strategy.（3）To further reduce the conservativeness of the fuzzy state estimation method,the above relaxation condition for the design of a joint multi-moment switching-type observer is also proposed.By designing a more comprehensive multi-moment gain scheduling mechanism,while removing the redundancy constraints of the traditional free matrix,the conservativeness is significantly reduced by maximising the incorporation of multi-moment normalized fuzzy weight function information into the fuzzy observer design.It is worth pointing out that although there is an increase in the number of free matrices introduced,the actual computational complexity is only slightly increased due to the reduced number of fuzzy cycles.