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

Luke Bhan; Miroslav Krstic; Yuanyuan Shi

eess.SYMar 31, 2026

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

Authors: Luke Bhan, Miroslav Krstic, Yuanyuan Shi

Organizations: Department of Electrical and Computer Engineering, University of California San Diego, La Jolla, CA 92093-0411, USA · Department of Mechanical and Aerospace Engineering, University of California San Diego, La Jolla, CA 92093-0411, USA

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.

Figures & tables

Panel of Figure 1 — Figure 1: Three-stage observer–predictor feedback law and corresponding horizons.

Figure 2: Example of feedback control for the problem in ( 84 ) with the FNO approximation of

\hat{\psi}

. The parameters for the delay function

D_{1}

were

(a_{1},b_{1},\alpha_{1},\omega_{1},\varphi_{1})=(0.4,0.31,-0.10,4.95,0.95)

and for

D_{2}

were

(a_{2},b_{2},\alpha_{2},\omega_{2},\varphi_{2})=(0.28,0.15,-0.06,1.28,0.82)

. The initial condition of the plant was

Z(0)=[-1,1]

and the observer

\xi(0)=[5,-5]

. The input history was fixed to ensure

0

input for the initial condition and the plant history was set to

Z(0)

for all times

t\leq 0

Feedback Control

Feedback control uses ongoing measurements to adjust actions, stabilize dynamical systems, track goals, and respond to disturbances and constraints.

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Department of Mechanical and Aerospace Engineering, The Ohio State University, Columbus, OH, USA. · Department of Chemical, Paper, and Biomedical Engineering at Miami University, Oxford, OH, USA. · Department of Mechanical and Manufacturing Engineering at Miami University, Oxford, OH, USA.

Mar 31, 2026J/K move · Enter open · S save

Sampling-Horizon Neural Operator Predictors for Nonlinear Control under Delayed Inputs

Luke Bhan, Peter Quawas, Miroslav Krstic, Yuanyuan Shi

The authors are with the University of California San Diego

Feedback Control Neural Operators

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Modern control systems frequently operate under input delays and sampled state measurements. A common delay-compensation strategy is predictor feedback; however, practical implementations require solving an implicit ODE online, resulting in intractable computational cost. Moreover, predictor formulations typically assume continuously available state measurements, whereas in practice measurements may be sampled, irregular, or temporarily missing due to hardware faults. In this work, we develop two neural-operator predictor-feedback designs for nonlinear systems with delayed inputs and sampled measurements. In the first design, we introduce a sampling-horizon prediction operator that maps the current measurement and input history to the predicted state trajectory over the next sampling interval. In the second design, the neural operator approximates only the delay-compensating predictor, which is then composed with the closed-loop flow between measurements. The first approach requires uniform sampling but yields residual bounds that scale directly with the operator approximation error. In contrast, the second accommodates non-uniform, but bounded sampling schedules at the cost of amplified approximation error, revealing a practical tradeoff between sampling flexibility and approximation sensitivity for the control engineer. For both schemes, we establish semi-global practical stability with explicit neural operator error-dependent bounds. Numerical experiments on a 6-link nonlinear robotic manipulator demonstrate accurate tracking and substantial computational speedup of 25

\times

over a baseline approach.

Abstract

Feedback Control

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