Sliding Mode Control for Uncertain Systems with Time-Varying Delays via Predictor Feedback and Super-Twisting Observer

TL;DR

This paper presents a robust sliding mode control method for uncertain linear systems with time-varying delays, using predictor feedback and a Super-Twisting observer to handle unmeasured states and disturbances.

Contribution

It introduces a combined predictor and Super-Twisting observer framework for stabilization of delayed, uncertain systems without assuming known disturbance models.

Findings

Effective delay compensation demonstrated through simulations

Robustness against parametric uncertainties validated

Stable control achieved despite unmeasured states and disturbances

Abstract

This paper introduces a novel stabilization control strategy for linear time-invariant systems affected by known time-varying measurement delays and matched unknown nonlinear disturbances, which may encompass actuator faults. It is considered that part of the state vector is not available for real-time measurement. To address this, the proposed approach combines an open-loop predictor with a state observer designed using the Super-Twisting Algorithm, aiming to compensate for the delays and estimate the unmeasured state components. Specifically, the nonlinear observer-based framework enables the reconstruction of unmodeled fault signals without assuming that they originate from a known exogenous system, offering robustness against parametric uncertainties. Meanwhile, the predictor forwards the delayed output in time. Subsequently, a sliding mode control law is formulated to enforce an ideal sliding mode and ensure global stabilization, even under a broader class of perturbations, unmodeled disturbances, parametric uncertainties, and delays, owing to the integration of the Super-Twisting observer. Numerical simulations illustrate the efficiency of the proposed approach.