Finite-time Filter Design For Conic-type Nonlinear For Stochastic Systems

In the process of industrial system,the mathematical model neglecting the nonlinear effect often generates the errors in the modeling process.Therefore,the model can not meet the requirements of modern industry for system performance.Conic-type nonlinearity is a special kind of nonlinearity,which is located in a hypersphere.And the center is described by one linear system,the radius is described by another linear system.Many engineering nonlinearities can be expressed by conic-type nonlinearities,such as local sinusoidal nonlinearities,saturation nonlinearities,dead-zone nonlinearities,piecewise linear functions,etc.Since many engineering nonlinear problems need to consider the influence of uncertainty such as parameters,structure,etc.,the filtering problem of nonlinear systems has been paid much attention.Switched systems is a typical hybrid system,which is composed of two levels of control system.The lower level control system is a series of finite number of subsys-tems,while the higher level control system is the switching law of these subsystems.It is because of this special structure that the switching system show excellent modeling ability in the control process of multi-mode systems.As another kind of hybrid system,Markov jump systems shows strong modeling ability for systems with structural muta-tions caused by external noise interference,sudden failure and maintenance of working components,etc.Through the analysis of the Markov jump systems,we first consider the case when the transition probability in the Markov chain is not constant,and the dwell time in it is no longer a fixed number.This leads to the concept of semi-Markov jump systems.On the other hand,we consider the situation that the controller or filter cannot acquire the system mode information in real time,and then the concept of hidden Markov model is introduced.For these two kinds of different Markov jump systems,we solve the filtering problem with conic-type nonlinearity,respectively.In practical engineering applications,we pay more attention to the dynamic char-acteristics of the system in a certain period of time rather than in an infinite interval for the short-time operating system,such as,robot system,missile system and chemical reaction.Considering the finite-time theory can be used to describe the transient per-formance of the system in the finite-time region,the research on the finite-time problem of the system is always a hot spot in the field of engineering control.In this thesis,the finite-time filtering theory of nonlinear stochastic systems is further studied in terms of summarizing the existing research results.The nonlinear stochastic system is taken as the research object,and the influence of uncertainty factors is also considered.Employ Lyapunov function,linear matrix inequality method and other processing methods to design finite-time filters over the finite-time region.The main research results of this thesis are highlighted as:(1)The finite-time L_? filtering problem of the conic-type nonlinear switched systems is studied.Under the condition that the input energy of external disturbance is bounded and the filter itself is uncertain,we design a finite-time L_?non-fragile filter.Through the analysis of the reconstructed dynamic filter error system,sufficient conditions are proposed to make the system finite-time bounded and satisfy the L_?performance index.(2)The finite-time L₂-L_? filtering problem of the conic-type nonlinear semi-Markov jump systems is studied.For the system with external interference,a finite-time L₂-L_?filter is designed.By selecting an appropriate Lyapunov function,we give sufficient conditions presented by some linear matrix inequalities to make sure the system is finite-time bounded.(3)The finite-time asynchronous L_? filtering problem of the conic-type nonlinear Markov jump systems is studied.The hidden Markov model is used to characterize the asynchronous phenomenon between the system mode and the filter mode.Then,through the analysis of the reconstructed mathematical model,sufficient conditions are proposed to make the error dynamic system finite-time bounded and satisfy the givenL_?performance index.