2020/12/04 by Mohammad Baharloo, Jalal Arabneydi, Baharloo, Mohammad M. +3 · 1 citation
Computer Science · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Distributed Control Multi-Agent Systems #FOS: Mathematics #Neural Networks Stability and Synchronization #Opinion Dynamics and Social Influence #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.2012.02838
openalex publication_date 2020/12/04 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
This paper investigates a soft-constrained MinMax control problem of a\nleader-follower network. The network consists of one leader and an arbitrary\nnumber of followers that wish to reach consensus with minimum energy\nconsumption in the presence of external disturbances. The leader and followers\nare coupled in the dynamics and cost function. Two non-classical information\nstructures are considered: mean-field sharing and intermittent mean-field\nsharing, where the mean-field refers to the aggregate state of the followers.\nIn mean-field sharing, every follower observes its local state, the state of\nthe leader and the mean field while in the intermittent mean-field sharing, the\nmean-field is only observed at some (possibly no) time instants. A social\nwelfare cost function is defined, and it is shown that a unique saddle-point\nstrategy exists which minimizes the worst-case value of the cost function under\nmean-field sharing information structure. The solution is obtained by two\nscalable Riccati equations, which depend on a prescribed attenuation parameter,\nserving as a robustness factor. For the intermittent mean-field sharing\ninformation structure, an approximate saddle-point strategy is proposed, and\nits converges to the saddle-point is analyzed. Two numerical examples are\nprovided to demonstrate the efficacy of the obtained results.\n