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

2026-03-30

AI Summary

This study addresses the challenge of real-time control for nonlinear systems subject to input delays and state sampling. It introduces neural operators into predictive feedback design for the first time, proposing two distinct schemes: one constructs a state trajectory prediction operator under uniform sampling, while the other approximates only the delay-compensating predictor under non-uniform sampling and composes it with the closed-loop flow. Theoretical analysis establishes an explicit relationship between neural operator approximation error and semi-global practical stability, revealing an engineering trade-off between sampling flexibility and error sensitivity. Experimental validation on a six-link nonlinear robotic manipulator demonstrates high-precision trajectory tracking, with a 25-fold improvement in computational speed over baseline methods.

Abstract

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.

Problem

• input delay
• sampled measurements
• predictor feedback
• nonlinear control
• computational tractability

Innovation

• neural operator
• predictor feedback
• input delay
• sampled measurements
• nonlinear control