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

2026-03-30

AI Summary

This work addresses the challenge of accurately computing the prediction horizon in linear systems with time-varying input and measurement delays, where the inverse of the delay function typically lacks a closed-form solution. To overcome this limitation, the paper introduces neural operators into predictive control for the first time, proposing a data-driven approach that combines numerical integration with neural operators to approximate the delay inverse function to arbitrary precision. Based on this approximation, an output-feedback predictive controller is constructed. Theoretical analysis demonstrates that the closed-loop system is globally exponentially stable provided the approximation error is sufficiently small. Numerical experiments further validate the method’s ability to effectively balance accuracy and computational efficiency.

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.

Problem

• time-varying delays
• predictor feedback
• output-feedback control
• prediction horizon
• inverse delay mapping

Innovation

• predictor feedback
• time-varying delays
• neural operators
• output-feedback control
• inverse delay mapping