Predicting the future state of disturbed LTI systems: A solution based on high-order observers

TL;DR

This paper introduces a method using high-order observers to predict the future states of disturbed linear time-invariant systems, addressing the challenge of unknown external disturbances affecting state prediction accuracy.

Contribution

The paper proposes a novel observer-based approach for predicting future states of disturbed LTI systems, including design methodologies to minimize prediction errors.

Findings

Effective prediction of future states under unknown disturbances

Comparison shows improved accuracy over existing methods

Design guidelines for high-order observers provided

Abstract

Predicting the state of a system in a relatively near future time instant is often needed for control purposes. However, when the system is affected by external disturbances, its future state is dependent on the forthcoming disturbance; which is, in most of the cases, unknown and impossible to measure. In this scenario, making predictions of the future system-state is not straightforward and, indeed, there are scarce contributions provided to this issue. This paper treats the following problem: given a LTI system affected by continuously differentiable unknown disturbances, how its future state can be predicted in a sufficiently small time-horizon by high-order observers. Observer design methodologies in order to reduce the prediction errors are given. Comparisons with other solutions are also established.