Sliding Mode Control Techniques for Nonlinear and Uncertain Systems

Sliding mode control represents a robust methodology for managing nonlinear systems subject to uncertain dynamics and external disturbances. Central to this approach is the design of a sliding surface—a manifold in the system’s state space—across which the controlled trajectory is driven and maintained, ensuring invariance against matched uncertainties. Classical first-order sliding mode control achieves robustness via discontinuous control actions, but is prone to chattering. Higher-order schemes, including supertwisting algorithms, address chattering by smoothing the control discontinuity while preserving finite-time convergence. Terminal sliding mode control further refines convergence to ensure that tracking errors reach zero in a finite or fixed time, often through fractional-power terms. Recent advances integrate adaptive disturbance observers, multiple sliding surfaces and discrete-time implementations to cope with both matched and unmatched uncertainties, control saturation and platform-specific challenges such as robotic manipulators and electric vehicle stability. Across aerospace, automotive and industrial settings, sliding mode techniques continue to deliver strong robustness, fast transient response and design flexibility, fostering global uptake in safety-critical applications.

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Generalised supertwisting algorithms have emerged to mitigate chattering while guaranteeing finite-time convergence. By replacing the conventional discontinuous term with a fractional-power component and tuning gains alongside the power exponent, these methods achieve smoother control trajectories without sacrificing robustness. Rigorous Lyapunov analyses establish that sliding variables converge to an arbitrarily small neighbourhood of the origin within finite time, with simulation studies demonstrating superior performance over classical supertwisting schemes.

Foundational surveys of terminal sliding mode control have synthesised decades of developments, from asymptotic stability to finite-time convergence and nonsingularity. These overviews articulate design principles for terminal sliding surfaces incorporating fractional-power dynamics, highlight strategies to suppress chattering and discuss integration of integral-type surfaces for enhanced disturbance rejection. Moreover, they identify open challenges in adaptive tuning, output-feedback realisation and practical implementation in resource-constrained platforms.

Novel fixed-time nonsingular fast terminal sliding mode controllers, augmented with adaptive disturbance observers, demonstrate global convergence within a predefined bound independent of initial conditions. These composite schemes employ a disturbance observer to estimate and compensate unknown inputs, while a nonsingular sliding surface guarantees chattering-free dynamics. Lyapunov-based proofs confirm that both the sliding surface and closed-loop states reach the origin in a fixed time, and simulation results on benchmark inverted-pendulum and robotic systems validate the approach’s efficacy and energy efficiency.

Sliding Mode Control Techniques for Nonlinear and Uncertain Systems publication trend

The graph below shows the total number of articles in sliding mode control techniques for nonlinear and uncertain systems across all publications each year (not limited to Nature Index journals).

Technical terms

Sliding surface: A designated manifold in the state space on which system trajectories are constrained, ensuring robustness against matched uncertainties.

Chattering: High-frequency oscillations in control input due to discontinuous switching, which can excite unmodelled dynamics and cause wear.

Supertwisting algorithm: A second-order sliding mode scheme that smooths control discontinuities by employing integral action and finite-time convergence properties.

Terminal sliding mode control: A class of sliding mode methods that utilise fractional-power terms to guarantee finite-time convergence of tracking errors to zero.

Fixed-time convergence: A convergence property ensuring that error dynamics reach the sliding surface or equilibrium within a predefined time bound, independent of initial conditions.

References

1. A Generalized Supertwisting Algorithm. IEEE Transactions on Cybernetics (2023).
2. Terminal Sliding Mode Control An Overview. IEEE Open Journal of the Industrial Electronics Society (2020).
3. Conventional and high order sliding mode control. Journal of the Franklin Institute (2020).
4. Fixed-Time Sliding Mode Control for Uncertain Robot Manipulators. IEEE Access (2019).
5. A Fast Nonsingular Terminal Sliding Mode Control Method for Nonlinear Systems With Fixed-Time Stability Guarantees. IEEE Access (2020).
6. Discrete-Time Sliding-Mode Control With a Desired Switching Variable Generator. IEEE Transactions on Automatic Control (2019).
7. Direct yaw-moment control of electric vehicles based on adaptive sliding mode. Mathematical Biosciences and Engineering (2023).
8. Perturbation Observer-Based Robust Control Using a Multiple Sliding Surfaces for Nonlinear Systems with Influences of Matched and Unmatched Uncertainties. Mathematics (2020).
9. Novel Fixed-Time Nonsingular Fast Terminal Sliding Mode Control for Second-Order Uncertain Systems Based on Adaptive Disturbance Observer. IEEE Access (2020).
10. Design of a Non-Singular Adaptive Integral-Type Finite Time Tracking Control for Nonlinear Systems With External Disturbances. IEEE Access (2021).
11. Effective Disturbance Compensation Method Under Control Saturation in Discrete-Time Sliding Mode Control. IEEE Transactions on Industrial Electronics (2019).