Fractional-Order Control of Nonlinear Dynamical Systems
Summary
Fractional-order control extends classical control theory by employing derivatives and integrals of non-integer order to capture memory and hereditary effects intrinsic to many physical, biological and engineering processes. In the context of nonlinear dynamical systems, fractional operators offer enhanced modelling fidelity for phenomena such as viscoelasticity, anomalous diffusion and long-term dependence. Controllers designed in the fractional domain can simultaneously shape transient response and steady-state performance, providing additional degrees of freedom that often yield improved robustness against uncertainty, parameter variation and external disturbance. Recent advances have focused on synthesising adaptive, sliding-mode and fuzzy controllers that guarantee boundedness and convergence of tracking errors under minimal knowledge of system parameters. Applications span secure communications via synchronisation of chaotic oscillators, vibration suppression in mechanical structures, power-grid stabilisation and coordinated motion of multi-agent systems.
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Fractional-Order Control of Nonlinear Dynamical Systems publication trend
The graph below shows the total number of articles in fractional-order control of nonlinear dynamical systems across all publications each year (not limited to Nature Index journals).
Technical terms
Fractional calculus: Extension of differentiation and integration to non-integer orders, employed to describe systems with memory and long-range interactions.
Nonlinear dynamical system: A system whose evolution is governed by equations in which the change of state is a nonlinear function of current states and inputs.
Sliding mode control: A robust control technique that forces system trajectories onto a designed invariant manifold despite uncertainties or disturbances.
Lyapunov stability theory: A mathematical method for establishing the stability of an equilibrium by constructing energy-like functions that decrease along system trajectories.
Synchronisation: The process by which coupled or forced systems adjust their dynamics to exhibit a common temporal pattern or phase relationship.
References
- Synchronization of Fractional-Order Delayed Neural Networks Using Dynamic-Free Adaptive Sliding Mode Control. Fractal and Fractional (2023).
- A Fuzzy Control Strategy to Synchronize Fractional‐Order Nonlinear Systems Including Input Saturation. International Journal of Intelligent Systems (2023).
- Adaptive neural control of non‐linear fractional order multi‐agent systems in the presence of error constraints and input saturation. IET Control Theory and Applications (2022).
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