Control Strategies for Time-Delay Systems

Time-delay systems, in which the evolution of states or outputs depends on past values, arise in numerous fields ranging from networked control to biological regulation. Delays may be constant, time-varying or stochastic, and they can compromise stability, performance and robustness if unaddressed. Contemporary control strategies encompass predictor-based schemes that estimate future states, Lyapunov–Krasovskii functional approaches for deriving delay-dependent stability criteria, and observer-based methods to reconstruct unmeasured states or disturbances. Adaptive and neural network techniques have been developed to cope with unknown nonlinearities, while sliding-mode and disturbance-observer frameworks enhance resilience against unmodelled perturbations. Advances in sampled-data and discrete-time designs enable practical implementation on digital platforms. Collectively, these methodologies offer systematic means to guarantee asymptotic convergence, ensure ultimate boundedness and attenuate the adverse effects of delays, thereby underpinning reliable operation of industrial processes, teleoperation devices and automated transportation systems.

Research from Nature Portfolio

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Research from all publishers

A novel output-feedback predictor-based control approach for discrete-time systems with time-varying input delays has been proposed. By integrating an extended state observer, the method actively rejects external disturbances and achieves robust stabilisation under unknown but bounded delays while reducing synthesis complexity. Applications in sampled-data and digital controllers demonstrate improved disturbance attenuation and delay compensation.

The moment dynamics of linear systems subject to stochastic delays and additive noise have been characterised through a semi-discretisation technique. Mean and second-moment equations yield necessary and sufficient conditions for mean-square stability. Case studies, including a connected automated vehicle model, illustrate how probabilistic delay profiles influence performance and guide controller tuning for enhanced robustness.

State-prediction-based control schemes for nonlinear systems facing input delays and external disturbances employ dynamic surface control combined with disturbance observers. Extensions cater to constant and time-varying delays, incorporate input saturation handling and guarantee semi-global ultimate uniform boundedness. Simulations on quadrotor unmanned aerial vehicles confirm the schemes’ efficacy in trajectory tracking under challenging delay and disturbance scenarios.

Control Strategies for Time-Delay Systems publication trend

The graph below shows the total number of articles in control strategies for time-delay systems across all publications each year (not limited to Nature Index journals).

Technical terms

Time-delay system: A dynamic system where the current state or output depends on past states or inputs after a fixed, variable or stochastic delay.

Predictor-based control: A control strategy that estimates future system states over the delay interval to compensate for time lags in feedback loops.

Lyapunov–Krasovskii functional: A generalised energy-like measure incorporating delay intervals, used to derive stability conditions for systems with delays.

Robust stability: The property by which a control system retains stability in the presence of model uncertainties, disturbances and delays.

Extended state observer: An estimator that reconstructs both system states and unknown disturbances to facilitate disturbance rejection and enhance control performance.

References

1. Output-feedback anti-disturbance predictor-based control for discrete-time systems with time-varying input delays. Automatica (2021).
2. On the moment dynamics of stochastically delayed linear control systems. International Journal of Robust and Nonlinear Control (2020).
3. State prediction based control schemes for nonlinear systems with input delay and external disturbance. IET Control Theory and Applications (2021).