An Information-State Based Approach to Linear Time Varying System Identification and Control

Abstract This paper considers the problem of system identification for linear time-varying systems. We propose a new system realization approach that uses an “information-state” as the state vector, where the information-state is composed of a finite number of past inputs and outputs. Using this framework, we develop a system identification algorithm that uses input–output data to fit an autoregressive moving average model (ARMA) to represent the current output in terms of finite past inputs and outputs. This information-state-based approach allows us to directly realize a state-space model using the estimated time-varying ARMA parameters for linear time-varying (LTV) systems. The paper develops the theoretical foundation for using ARMA parameters-based system representation using only the concept of linear observability, details the reasoning for exact output modeling using only the finite history, and shows that there is no need to separate the free and the forced response for identification. The paper also discusses the implications of using the information-state system for optimal output feedback control and shows that the solution obtained using a suitably posed information-state problem is optimal for the original problem. The proposed approach is tested on various different systems, and the performance is compared with state-of-the-art LTV system identification techniques.