Research On Fuzzy Control And Fault Estimation For Uncertain Nonlinear Systems

With the rapid development of modern manufacturing industry,the characteristics of uncertainty,nonlinearity,and diversity of controlled objects are becoming more and more obvious and severely restrict the further improvement of the stable operation level of the entire control system.In recent years,the stability analysis and control design of uncertain nonlinear systems have become a hot research topic in the field of control science and engineering.In particular,thanks to the technical advantages of fuzzy systems in the modeling of uncertain nonlinear systems where it is difficult to obtain accurate mathematical models,the stability analysis and control design research of uncertain nonlinear systems based on fuzzy models have achieved important progress.However,most of the existing methods generally use parallel distributed compensation(PDC)technology for stability analysis and control design of fuzzy control systems,resulting in high conservative theoretical results,which limits the widespread application of fuzzy control theory;The problem of fault estimation based on fuzzy model is also facing the same dilemma.In order to solve the above problems,this paper studies the fuzzy control and fault estimation of uncertain nonlinear systems,and proposes a Markovian jump fuzzy system(MJFS)robust control method with known transition probability,a discrete T-S fuzzy system real-time scheduling stabilization control method based on variable weight switching mechanism,and a fuzzy fault observer design method based on weighted switching method.Specifically,the main research contents of this paper are described as follows:Firstly,the Markovian jump fuzzy system is used to model the nonlinear system with multi-modal jump characteristics,and a non-PDC fuzzy state feedback controller based on a new switching mechanism is proposed.In this way,the relevant knowledge of the switching mechanism can be fully utilized,the normalization method is combined in the design of the controller,and a matching Lyapunov function is designed corresponding to this mechanism.Finally,a MJFS robust control method with known transition probability is given by introducing a set of relaxation matrix variables.The simulation results successfully verify that the method is less conservative than the previous related theoretical methods based on PDC technology.Secondly,the real-time scheduling stabilization control problem based on discrete-time T-S fuzzy system is studied.A new variable weight switching mechanism is proposed by effectively utilizing the normalized fuzzy weight function size ranking information at each sampling time.Based on this switching mechanism,a new fuzzy switching controller is designed,which has several different activation modes and can be dynamically adjusted by the output value of the variable weight switching mechanism at each sampling moment,thus significantly reducing the conservativeness of fuzzy control design.More importantly,the real-time scheduling stabilization control method for discrete T-S fuzzy systems based on variable weight switching mechanism does not need to add additional off-line or on-line computational burden while reducing the conservativeness of the control design of the existing methods.In other words,the proposed method has good performance characteristics,which increasing the adaptive range and algorithm efficiency of the theoretical method.Finally,the problem of fuzzy fault estimation based on discrete-time T-S fuzzy system is studied.The space generated by the normalized fuzzy weighting function is divided into several non-overlapping subspaces and an effective and fast weighting switching method is designed to identify the specific subspace of the system at each sampling time on line.On this basis,a switched fuzzy fault observer is proposed.It has different observer gain matrices in different subspaces,thus it can make full use of the characteristic information of the subspaces in which it is located,it is less conservative than the previous correlation results.More importantly,the online operation process of the switched fuzzy fault observer successfully eliminates some time-consuming online calculation burden of the previous method,which is also more conducive to the practical application of the theoretical method.