Pinning Control Techniques in Complex Dynamical Networks

Pinning control refers to a strategy whereby a select subset of nodes within a complex dynamical network is directly influenced by external inputs to induce desired collective behaviour such as synchronization, consensus or structural balance. By exploiting the interplay between network topology and nodal dynamics, pinning techniques enable efficient regulation of large-scale systems while minimising control effort. Key developments encompass continuous, intermittent and hybrid schemes, often underpinned by Lyapunov‐based stability analysis and linear matrix inequalities. Advances in adaptive pinning allow coupling strengths and pinned sets to be adjusted in real time to accommodate uncertainties, nonlinearities and time‐varying delays. Applications span power‐grid stabilisation, neural ensemble regulation, secure communication and coordination of unmanned aerial vehicles. Recent work has extended pinning frameworks to fractional‐order dynamics, directed topologies and multiplex architectures, highlighting their versatility in addressing robustness and scalability in real‐world networks.

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Recent studies have demonstrated robust pinning schemes in networks with fractional‐order dynamics. An aperiodically intermittent pinning control approach was applied to a directed fractional‐order network, where only a single node is intermittently controlled. Lyapunov function methods yielded sufficient conditions for complete synchronization despite memory effects inherent in fractional calculus. Numerical examples illustrated rapid convergence with minimal control duty cycles. A novel hybrid pinning adaptive control method addressed function projective synchronization in networks with mixed time‐varying and asymmetric coupling delays. By combining nonlinear and adaptive linear feedback, the scheme allowed dynamic adjustment of pinned node selection and coupling gain updates. Stability was ensured via tailored Lyapunov–Krasovskii functionals and parameter update laws, enabling drive–response networks to match prescribed scaling functions. Further work on hybrid adaptive pinning control for delayed neural networks with mixed uncertainties integrated adaptive laws to estimate unknown coupling parameters and determine optimal pinned nodes. The controller manipulated scaling functions to achieve function projective synchronization, while rigorous Lyapunov arguments established global convergence. Simulations confirmed effectiveness under uncertain asymmetric couplings and time‐varying delays.

Pinning Control Techniques in Complex Dynamical Networks publication trend

The graph below shows the total number of articles in pinning control techniques in complex dynamical networks across all publications each year (not limited to Nature Index journals).

Technical terms

Pinning control: A control strategy that directly actuates only a subset of nodes in a network to achieve global objectives.

Complex dynamical network: An assembly of interacting dynamical units (nodes) connected by edges that may vary in strength and topology.

Synchronization: The process by which network nodes align their states or outputs over time under coupling or control inputs.

Fractional‐order system: A dynamical system described by differential equations of non‐integer order, capturing memory and hereditary properties.

Lyapunov function: A scalar function employed to assess the stability of an equilibrium or synchronised state via its time derivative.

Adaptive control: A control methodology that updates controller parameters in real time to cope with model uncertainties or changing conditions.

References

1. Synchronization of fractional-order dynamical network via aperiodically intermittent pinning control. Advances in Continuous and Discrete Models (2019).
2. Modified function projective synchronization of complex dynamical networks with mixed time-varying and asymmetric coupling delays via new hybrid pinning adaptive control. Advances in Continuous and Discrete Models (2017).
3. Hybrid Adaptive Pinning Control for Function Projective Synchronization of Delayed Neural Networks with Mixed Uncertain Couplings. Complexity (2017).