Simultaneous Input and State Estimation for Systems With Arbitrary Inherent Delay

• 成果类型: Article
• 署名作者: Gakis, Grigorios; Smith, Malcolm C.
• 署名单位: University of Cambridge
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3637004
• 发表日期: 2026
• 关键词: RICCATI DIFFERENCE EQUATION; MINIMUM-VARIANCE INPUT

摘要

This article derives a filtering and a smoothing algorithm for simultaneous input and state estimation for linear discrete-time systems of any inherent delay. The exogenous input is assumed to be completely unknown and the only stochastic assumptions are on the output measurements and the initial state. The algorithm includes the Kalman filter which is itself a special case of a system with an inherent delay of zero. The derived recursions take a similar form to the Kalman filter, and are straightforward to implement. The approach uses a standard characterization of a system's inherent delay in terms of the incremental ranks of a sequence of Toeplitz matrices of Markov parameters. Two judiciously chosen rank decompositions of the relevant Toeplitz matrix corresponding to the inherent delay are used to develop the algorithm. Conditions for the convergence of the filter are also derived and consist of a controllability condition and a minimum phase condition. The article also presents a smoothing algorithm that can estimate the states and inputs of the system over a fixed time horizon. The theory is illustrated on a field controlled dc motor system with an inherent delay of two and a mass-spring-damper chain system with an inherent delay of five.