Control of coupled oscillator networks with application to microgrid technologies

Abstract

The control of complex systems and network-coupled dynamical systems is a topic of vital theoretical importance in mathematics and physics with a wide range of applications in engineering and various other sciences. Motivated by recent research into smart grid technologies we study here control of synchronization and consider the important case of networks of coupled phase oscillators with nonlinear interactions--a paradigmatic example that has guided our understanding of self-organization for decades. We develop a method for control based on identifying and stabilizing problematic oscillators, resulting in a stable spectrum of eigenvalues, and in turn a linearly stable synchronized state. Interestingly, the amount of control, i.e., number of oscillators, required to stabilize the network is primarily dictated by the coupling strength, dynamical heterogeneity, and mean degree of the network, and depends little on the structural heterogeneity of the network itself.

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• Collective dynamics of heterogeneously and nonlinearly coupled phase oscillators
• Neural Ordinary Differential Equation Control of Dynamics on Graphs
• Multilayer Network Science: from Cells to Societies
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• Optimal synchronization of directed complex networks
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• Collective frequency variation in network synchronization and reverse PageRank
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• Accelerating Optimal Experimental Design for Robust Synchronization of Uncertain Kuramoto Oscillator Model Using Machine Learning
• Geometric unfolding of synchronization dynamics on networks
• Synchronization of Network-Coupled Oscillators with Uncertain Dynamics
• Symmetry and symmetry breaking in coupled oscillator communities
• How do higher-order interactions shape the energy landscape?
• Target decoupling in a coupled optical system resistant to random perturbation
• Neural Message Passing for Objective-Based Uncertainty Quantification and Optimal Experimental Design
• Competitive Suppression of Synchronization and Non-Monotonic Transitions in Oscillator Communities with Distributed Time Delay
• Grass-roots optimization of coupled oscillator networks
• Fundamental building blocks of controlling complex networks: A universal controllability framework
• Greedy optimization for growing spatially embedded oscillatory networks