Newton-series-based observer-predictor control for disturbed input-delayed discrete-time systems

TL;DR

This paper introduces a Newton-series-based observer-predictor control method for discrete-time systems with input delays and unknown disturbances, enhancing prediction accuracy and disturbance attenuation through advanced observer design and LMI optimization.

Contribution

It proposes a novel Newton-series-based prediction approach combined with an extended Luenberger observer for improved state and disturbance estimation in delayed systems.

Findings

Enhanced prediction accuracy demonstrated in simulations.

Improved disturbance attenuation achieved with the proposed method.

Effective observer design using LMIs for minimized prediction errors.

Abstract

This paper deals with the problem of predicting the future state of discrete-time input-delayed systems in the presence of unknown disturbances that can affect both the state and the output equations of the plant. Since the disturbance is unknown, computing an exact prediction of the future plant states is not possible. To circumvent this problem, we propose using a high-order extended Luenberger-type observer for the plant states, disturbances, and their finite difference variables, combined with a new equation for computing the prediction based on Newton's series from the calculus of finite differences. Detailed performance analysis is carried out to show that, under certain assumptions, both enhanced prediction and improved attenuation of the unknown disturbances are achieved. Linear matrix inequalities (LMIs) are employed for the observer design to minimize the prediction errors. A stabilization procedure based on an iterative design algorithm is also presented for the case where the plant is affected by time-varying uncertainties. Examples from the literature illustrate the advantages of the scheme.