Dynamic event-triggered control for fixed-time synchronization of Kuramoto-oscillator networks with and without a pacemaker

Fixed‐time Synchronization of Stochastic Kuramoto‐Oscillator Networks With Switching Topology Under Dynamic Event‐triggered Scheme

“…It should be noted that the proposed scheme can also be extended to frequency synchronization problems of Kuramoto network. To achieve this object, we can follow the treatment given in References 18 and 44, where intermediate control variables are used. The controller is designed as $$$ {u}_i(t)={U}_i^1(t) $$$, and $$$ {\dot{U}}_i(t)=-{\rho}_1{\sum}_{j=1}^N{b}_{ij}{\left(\left(\dot{\theta_i}\left({t}_k^i\right)-{\dot{\theta}}_j\left({t}_k^i\right)\right)\ \right)}^{\gamma }-{\rho}_2{\sum}_{j=1}^N{c}_{ij}\tanh \left(\gamma \left({\dot{\theta}}_i\left({t}_k^i\right)-{\dot{\theta}}_j\left({t}_k^i\right)\right)\right)-{\rho}_3{\...$…”

“…• Different from existing results that investigate the fixed-time synchronization problem under an idealized assumption without stochastic noise and time-invariant topology, 19,44 we provide the solution for stochastic noise and switching topology with a multilayered structure, and we propose a more robust distributed control approach.…”

“…By constructing a Lyapunov function of the measurement error, we also prove that the Zeno behavior is excluded. The main contributions are summarized as follows:Different from existing results that investigate the fixed‐time synchronization problem under an idealized assumption without stochastic noise and time‐invariant topology, 19,44 we provide the solution for stochastic noise and switching topology with a multilayered structure, and we propose a more robust distributed control approach. Compared to our previous work using static event‐triggered methods in References 27 and 28, and the conventional time‐triggered method, 43 our approach with dynamic event‐triggered scheme guarantees fixed‐time phase agreement within the desired time and conserves more communication and computation resources. …”

Stochastic synchronization of Kuramoto-oscillator network with pinning control

“…The mathematical principles behind complex networks can be better understood from the perspective of network dynamics. As the most common collective behavior in network dynamics, synchronization plays an important role in systems engineering [4], ecology [5], and other fields [6][7][8]. Therefore, it is critical to study the intrinsic mechanisms of synchronization phenomena, both in theory and in practice.…”

Fixed/Preassigned-Time Synchronization of Fuzzy Memristive Fully Quaternion-Valued Neural Networks Based on Event-Triggered Control

“…The dynamic event-triggering mechanism allows the triggering conditions to adjust dynamically with time and changes in system state, which can further save resources while maintaining or enhancing system performance. By introducing dynamic variables, the control system can adjust the event-triggering rules based on real-time system performance and predetermined stability requirements, thus increasing the interval between executions and reducing unnecessary control updates while ensuring stability and performance metrics [36][37][38][39].…”