Distributed optimal consensus for stochastic fractional-order multi-agent systems: Frequency distribution model approach

Optimal consensus of multi-agent systems under stochastic disturbances yields valuable insights into improving collaborative efficiency, resource utilization, and system robustness amidst uncertain environments. This study focuses on achieving optimal consensus in fractional-order multi-agent systems (FOMASs) with additive noises, an emerging research area with significant theoretical and practical implications, which deepens our understanding of system behavior and supports precise modeling and control strategy development. First, we introduce an innovative approach using a frequency distribution model to bridge fractional-order and integer-order systems, deriving sufficient conditions for Lyapunov stability. Second, we establish and address an optimal control problem tailored for stochastic Caputo fractional-order systems, laying the foundation for exploring the balance between control performance and robustness in the presence of stochastic perturbations and fractional-order dynamics. Additionally, we tackle optimal consensus control problems for stochastic FOMASs, providing sufficient conditions for achieving optimal mean square consensus through optimal control strategies and consensus conditions. The complexity of solution expressions is heightened by the presence of random variables. Finally, practical applicability is demonstrated by applying these findings to the distributed circuits and battery circuit equalization problem, thereby expanding the application potential of fractional-order systems in renewable energy.