Fuzzy Sliding Mode Control for Nonlinear Systems
Summary
Fuzzy sliding mode control (FSMC) integrates the robustness of sliding mode control with the adaptability of fuzzy logic to govern nonlinear dynamic systems under uncertainty. By representing a complex plant through a Takagi–Sugeno fuzzy model, the overall control design decomposes the nonlinear dynamics into a convex blend of linear subsystems. Local sliding surfaces are defined for each rule consequents and then aggregated into a global manifold, ensuring finite-time convergence and strong disturbance rejection. Fuzzy inference adjusts switching gains in real time to mitigate chattering while accommodating time-varying uncertainties and external perturbations. Stability and performance specifications are enforced via Lyapunov-based functions and translated into tractable linear matrix inequalities. FSMC has found applications in robotics, automotive systems, power electronics and bio-economic networks, where precise tracking and resilience to disturbances are critical. Recent innovations include observer-based sliding mode schemes to estimate unmeasurable states, multi-surface back-stepping architectures for strict-feedback structures and terminal sliding formulations for accelerated settling.
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Researchers have developed a multi-surface back-stepping sliding mode control framework for uncertain nonlinear systems in strict-feedback form using a Takagi–Sugeno fuzzy model. Multiple local sliding surfaces are combined via convex weights, and optimal gain matrices are obtained through a generalised eigenvalue problem. Adaptive update laws estimate bounds on matched and unmatched uncertainties, while H₂-optimisation and α-stability regions enhance transient performance. All design conditions are cast as linear matrix inequalities and validated on practical examples, demonstrating robust tracking under external disturbances.
An observer-based fuzzy sliding mode scheme has been proposed for discrete-time Takagi–Sugeno Markov jump systems subject to imperfect premise matching. Two fuzzy switching manifolds are constructed for the disturbance estimator and the sliding mode observer. A linear matrix inequality criterion guarantees robust admissibility under H∞ performance requirements and ensures reachability of the sliding surfaces. Numerical case studies on bio-economic and tunnel diode circuits confirm the effectiveness of the approach in the presence of unmeasured states and external perturbations.
An adaptive terminal sliding mode control strategy for T–S fuzzy-based nonlinear systems introduces a dynamic terminal sliding surface to achieve finite-time convergence. The two-stage design first uses linear matrix inequalities to derive a state feedback gain satisfying H₂-performance and partial eigenstructure assignment. Subsequently, control effort and actuator uncertainty bounds inform a convex optimisation step to compute the dynamic sliding gain. Reformulating the terminal controller in strict-feedback form enables output-tracking applications. Comparative simulations highlight faster settling and reduced control effort relative to traditional schemes.
Fuzzy Sliding Mode Control for Nonlinear Systems publication trend
The graph below shows the total number of articles in fuzzy sliding mode control for nonlinear systems across all publications each year (not limited to Nature Index journals).
Technical terms
Takagi–Sugeno fuzzy model: A representation of a nonlinear system as a weighted combination of linear subsystems using fuzzy membership functions.
Sliding mode control: A robust control method that drives the system state to a predefined sliding surface and maintains motion along that surface.
Sliding surface: A hypersurface in the state space defined so that trajectories confined to it exhibit desired closed-loop dynamics.
Lyapunov stability: A criterion using a scalar energy-like function to assess the convergence and robustness of a control system.
Linear matrix inequality (LMI): A convex constraint on matrix variables used to encode stability and performance conditions in control design.
References
- A Fuzzy Design for a Sliding Mode Observer-Based Control Scheme of Takagi-Sugeno Markov Jump Systems under Imperfect Premise Matching with Bio-Economic and Industrial Applications. Mathematics (2022).
- Adaptive Optimal Multi-Surface Back-Stepping Sliding Mode Control Design for the Takagi-Sugeno Fuzzy Model of Uncertain Nonlinear System With External Disturbance. IEEE Access (2022).
- Adaptive Optimal Terminal Sliding Mode Control for T‐S Fuzzy‐Based Nonlinear Systems. Complexity (2024).
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