A Krein Space Approach to H-infinity Filtering of Discrete-Time Nonlinear Systems

作者：Zhong Maiying^*; Guo Dingfei; Zhou Donghua

来源：IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS, 2014, 61(9): 2644-2652.

DOI：10.1109/TCSI.2014.2333352

• H-infinity nonlinear filter
• indefinite quadratic form
• Krein space
• projection
• Riccati recursion

In this paper, a Krein space approach to finite horizon H-infinity filtering is proposed for a class of affine nonlinear discrete-time systems. It is shown that the problem of H-infinity nonlinear filtering can be converted into a minimum of an indefinite quadratic form. Hence, a relationship between H-infinity nonlinear filter in Hilbert space and nonlinear estimation in Krein space is established. By using first-order Taylor approximation and Krein space projection, a sufficient and necessary condition for the minimum is derived. Moreover, a feasible solution of the H-infinity nonlinear filter can be obtained by recursively computing Riccati recursions. Finally, a numerical example and one kind of integration filter are used to demonstrate the effectiveness of the proposed method.

• 出版日期2014-9
• 单位清华大学; 北京航空航天大学