Predictor-Based Output-Feedback Control of Linear Systems with Time-Varying Input and Measurement Delays via Neural-Approximated Prediction Horizons

TL;DR

This paper introduces neural-approximated prediction horizons for predictor feedback control of linear systems with time-varying delays, ensuring stability and demonstrating practical effectiveness through numerical experiments.

Contribution

It formulates the inverse delay mapping as an operator learning problem and develops neural operator-based methods for approximation, enabling stable output-feedback control.

Findings

Both neural and numerical methods achieve arbitrary approximation accuracy.

The proposed control scheme guarantees global exponential stability.

Numerical experiments validate the effectiveness and trade-offs of the methods.

Abstract

Due to simplicity and strong stability guarantees, predictor feedback methods have stood as a popular approach for time delay systems since the 1950s. For time-varying delays, however, implementation requires computing a prediction horizon defined by the inverse of the delay function, which is rarely available in closed form and must be approximated. In this work, we formulate the inverse delay mapping as an operator learning problem and study predictor feedback under approximation of the prediction horizon. We propose two approaches: (i) a numerical method based on time integration of an equivalent ODE, and (ii) a data-driven method using neural operators to learn the inverse mapping. We show that both approaches achieve arbitrary approximation accuracy over compact sets, with complementary trade-offs in computational cost and scalability. Building on these approximations, we then develop an output-feedback predictor design for systems with delays in both the input and the measurement. We prove that the resulting closed-loop system is globally exponentially stable when the prediction horizon is approximated with sufficiently small error. Lastly, numerical experiments validate the proposed methods and illustrate their trade-offs between accuracy and computational efficiency.