Pareto Optimal Filter Design For Stochastic Systems Via H₂/H_∞ Optimization

With the development of science and technology,the traditional filter and some existing modern filters are not enough to solve many problems in the field of biology and engineering.The proposal of Pareto optimization has gradually attracted the attention of the majority of scholars,and the construction of a new filter is of great research significance.In addition,the general stochastic systems with perturbation and multiplicative noise and Markov jump system in dynamic systems are worth studying.The design of relevant optimal filters for these systems have attracted wide attention in recent years.In this thesis,the Pareto optimal filter design problems of H₂/H_∞ optimiza-tion for a general stochastic systems with multiplicative noises and a simple Markov jump system are studied.It mainly includes the following contents:The first chapter mainly introduces the background and significance of fil-ter design,gives a brief introduction to filter, H₂/H_∞ optimization and Linear Markov jump system,explains the practical significance of Pareto optimization.In Chapter 2,for a general stochastic linear system with multiplicative noise,through constructing a filter,we can got a filtering error estimation system.For the Pareto optimal filter design problem via the mixed H₂/H_∞ optimization,the upper bound-s of two performance indexes of₂andH_∞optimization are given respectively,and it is necessary to find a suitable gain matrixK^*to make the two performance indexes achieve the optimal simultaneously.It is necessary to study the filter error estimation system,so that the signal estimation error can achieve both the opti-mal mean square error and the robustness of the optimal filter.Therefore,it is necessary to convert the research problems into equivalent ones,and convert the inequality constraint problem into the Pareto optimal inequality problem with L-MI constraint by using the definition of Pareto optimal.LMI toolbox in MATLAB can be used to solve LMIs and obtain the required results.In Chapter 3,when the transfer probability matrix of MJLs is known,the stability and performance indexes of the system are discussed,and the design problem of Pareto optimal filter based on H₂/H_∞ is studied.Then,the results of Chapter 2 are extended by using the equivalent transformation method.