Research On Robust Filtering Of Switched Hybrid System

With the increasing complexity and integration level of the fields that people dabbled, the need of describing systems and solving problems is bombing. The switched hybrid system is an effective mathematic model to describe complex systems; a series of sub-systems and a serial of switched numbers make it up. In addition, the sub-systems could be by discrete-time systems, continuous-time systems and mix-time systems. The switching rule is to describe the system trajectory, which might be desired by the system itself, and could be controlled. The discrete-time switched system is one kind of switched hybrid system, and all of its sub-systems are discrete-time systems, so it close to the computer controls system. Now the research on discrete-time is a hot issue all over the world.The problem of optimal filtering or state estimation has been extensively investigated for more than two decades in various branches of science and engineering, such as computer vision, communications, navigation and tracking systems. H infinite filtering method is a widely used robust filtering approach; it could solve the filtering problem in systems, which have uncertainties and undesirable noisy. The linear matrix inequality(LMI) approach has been used in many theoretical researches and industrial processes to calculate the parameters in H_∞ filtering,and of course in this paper, the LMI method is used to solve the problem which related to switched hybrid systems. In addition, when it comes to the discrete-time system, the method with Riccati faction is useful. Kalman filtering is a typical filtering method and has been widely used, it analyses the system state by the state space approach, and it could filter the system state from the white noise. However, at the same, the Kalman filtering could not solve the system with uncertainties, and it has bad performance when it deals with non-linear systems. So in this paper, a new variable is introduced to describe the boundary of error covariance, and use it to depress the noise and uncertainties in the systems. In addition, the extend Kalman filtering is to fix the Kalman algorithm to adopt the non-linear systems. The unscented Kalman filtering uses another method, UT transformation to solve the non-linear problem. Moreover, the unscented Kalman filtering should calculate more points’ value, so it needs more software resource and hardware resource.In the first chapter, there is the introduction of switched hybrid system and discrete-time switched system, especially the information of basic rules and researches abroad and native. Moreover, the content of the second chapter is about the stability of the switched hybrid system and discrete-time switched system, in order to lean the mathematic model close to the practical circumstances, this chapter discusses the robust stability of the switched hybrid system and discrete-time switched system. Then in chapter 3 and 4, two typical filtering methods, Kalman filtering and H_∞ filtering, have been discussed, and in the end of these two chapters, some simulating examples have been illustrated to prove the feasibility of the filtering method, and the rationality of the approach to get the parameters. The figures of the illustration are rational and convincing.