Finite-Time Control of Chaotic Systems with Uncertainties
Summary
Chaos arises in many nonlinear physical, biological and engineering systems when high sensitivity to initial conditions and parameter variations produce seemingly random trajectories. In real-world applications, uncertainties in model parameters, external disturbances and actuator limitations challenge the stabilisation and synchronisation of such chaotic dynamics. Finite-time control seeks to drive these unstable trajectories to desired states within a guaranteed time bound, combining speed with robustness. Recent advances blend adaptive techniques, sliding mode control and disturbance observers to manage unknown nonlinearities, delays and fractional-order dynamics. Terminal sliding mode methods ensure chattering reduction while disturbance-observer frameworks estimate and compensate for perturbations, yielding rapid convergence. These strategies underpin secure communication via chaotic masking, precise vibration suppression in MEMS resonators, robust trajectory tracking in aerospace vehicles and stabilisation of power systems. By ensuring predictable settling times and resilience to uncertainties, finite-time control of chaotic systems holds promise for next-generation technologies requiring fast, reliable and secure dynamical regulation.
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Finite-Time Control of Chaotic Systems with Uncertainties publication trend
The graph below shows the total number of articles in finite-time control of chaotic systems with uncertainties across all publications each year (not limited to Nature Index journals).
Technical terms
Finite-time stability: Convergence of system states to equilibrium within a predetermined finite time.
Chaotic system: A dynamical system exhibiting high sensitivity to initial conditions and complex, bounded trajectories.
Fractional-order system: A system characterised by derivatives of non-integer order, capturing memory and hereditary properties.
Sliding mode control: A robust control method driving system dynamics onto a defined manifold to reject uncertainties.
Disturbance observer: A dynamic estimator designed to reconstruct and compensate for unknown perturbations affecting the system.
Generalised synchronization: A coordination regime where a response system follows the trajectory of a drive system under a functional relationship.
References
- An Integral Sliding Mode Control of Uncertain Chaotic Systems via Disturbance Observer. Complexity (2021).
- Finite-time generalized synchronization of non-identical fractional order chaotic systems and its application in speech secure communication. PLOS ONE (2022).
- Stabilization of Nonlinear Vibration of a Fractional-Order Arch MEMS Resonator Using a New Disturbance-Observer-Based Finite-Time Sliding Mode Control. Mathematics (2023).
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