Research On Robust Filtering For Complex Uncertain Discrete-time Systems

Reviewing the research of robust filtering design in the latest decade, Krein spaceestimation has been recognized and has been becoming into a novel researching field ofrobust filter design. Krein space approach is an essential method of filtering design to declinefilter design complexity, to enhance filter precision, and to fulfill practicality. Then this paperfocuses on Krein space approach to filter design for some classes of uncertain systems thatinvolve linear systems and nonlinear systems. Through this work, it is expected to improveKrein space method theory and to expand its research area. And the effectiveness of theproposed Krein space filter are supported through tests and comparations in numbericalexamples using Matlab. The main work of this paper is as follows.Firstly, this paper studies novel design ideas of Krein space filtering for some classes oflinear uncertain systems. Uncertain parameter and multiplicative noise are respectivelyconsidered existing in both state and measurement equations. In premise of introducing nonon-zero factor into objective problem, novel Krein space formal state-space systems aredesigned. As a result, the hidden trouble that non-zero factor might leads to large error iseliminated.Robust Kalman filter and robust H_∞filter are design respectively in the case of knownand unknown noise characteristics. Firstly,H2-indexed quadratic form and H_∞-indexedquadratic form are given respectively from the sum quadratic constraint(SQC) and robustH_∞problem. Secondly, the column of the objective quadratic form are expanded throughsome equivalent transformation to contain at least all vectors in the original system. In fact,the inverse of central weight matrix is the central of error Gramian in Krein space. Lastly,Krein space formal state-space system can be given according to the original system and thequadratic form. The effectiveness of the proposed filters are testified through Matlabsimulations.Secondly, this paper proposes novel design ideas of Krein space filtering for someclasses of linear uncertain state-delay systems. Delay-independent filtering is developed totime-varying delay systems, while delay-dependent filtering is investigated to constant delaycases in order to improve filter precision. This paper researchs delay systems including casesof constant delay, time-varying delay, and multiple delays.In the case that time-varying delay(whatever single or multiple) exists in both state and measurement equations, a novel method is proposed to design Krein space delay-independentfilter. The state-delay is regarded into the Krein space formal noise column, and accordingly,the quadratic form has to be equivalently transformed.In the constant-delay case, a novel method is developed to design Krein spacedelay-dependent filter. The delayed state is regarded as a state vector in the augmented Kreinspace formal system. Meanwhile, state column in quadratic form is augmented throughappropriate initial conditions. Then Krein space formal system can be determined throughoriginal system and the quadratic form. The Matlab simulations show that the proposed Kreinspace filters are robustness and stable with enhancing precision.Thirdly, this paper proposes novel design ideas of Krein space filtering for some classesof nonlinear uncertain systems. This paper investigates robust EKF for nonlinear uncertainsystems, then proposes robust H_∞filtering for the case that noise characteristics areunknown. At last, a novel method without augmenting state is attempted to designdelay-dependent filtering for nonlinear uncertain time-delay systems. The effectiveness of theproposed filters are all verified through Matlab simulations.Considering the computational burden risk in the delay-dependent filter design for linearsystems, this paper tries to study a novel Krein space filter design without augmenting statesfor nonlinear uncertain time-delay systems. Both delayed state and nonlinear function aredevided into two parts(posteriori estimate and posteriori error), each part of which will behandle separately. Existance condition and Ricatti recursions of the proposed robust H_∞filtering are both given, and two numberical examples shows the effectiveness.