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

TL;DR

This paper introduces an information-state based method for identifying and controlling linear time-varying systems, leveraging finite past inputs and outputs to directly realize state-space models and optimize output feedback control.

Contribution

It proposes a novel system realization approach using an information-state composed of past data, enabling direct ARMA-based modeling and control of LTV systems without separating free and forced responses.

Findings

The approach accurately models LTV systems using finite data history.

It provides a theoretically sound basis for using ARMA parameters in system realization.

Performance comparisons show advantages over existing LTV identification methods.

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. The system identification algorithm 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 paramters 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.