Robustness of Prediction Based Delay Compensation for Nonlinear Systems

TL;DR

This paper demonstrates that prediction-based delay compensation schemes for nonlinear systems inherently possess robustness properties, ensuring stability despite delays and packet losses, especially when the nominal system is ISS.

Contribution

It proves that prediction-based delay compensation schemes are robust if the nominal system is ISS, and analyzes how the prediction horizon affects robustness.

Findings

Prediction-based delay compensation schemes are inherently robust.

Robustness depends on the prediction horizon.

Simulation confirms theoretical robustness results.

Abstract

Control of systems where the information between the controller, actuator, and sensor can be lost or delayed can be challenging with respect to stability and performance. One way to overcome the resulting problems is the use of prediction based compensation schemes. Instead of a single input, a sequence of (predicted) future controls is submitted and implemented at the actuator. If suitable, so-called prediction consistent compensation and control schemes, such as certain predictive control approaches, are used, stability of the closed loop in the presence of delays and packet losses can be guaranteed. In this paper, we show that control schemes employing prediction based delay compensation approaches do posses inherent robustness properties. Specifically, if the nominal closed loop system without delay compensation is ISS with respect to perturbation and measurement errors, then the closed loop system employing prediction based delay compensation techniques is robustly stable. We analyze the influence of the prediction horizon on the robustness gains and illustrate the results in simulation.