2020/12/02 by Jalal Arabneydi, Arabneydi, Jalal, Aditya Mahajan +1 · 2 citations
Economics, Econometrics and Finance · Engineering · #FOS: Mathematics #Optimization and Control (math.OC) #Stability and Control of Uncertain Systems #Stability and Controllability of Differential Equations #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2012.02052
openalex publication_date 2020/12/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A decentralized control system with linear dynamics, quadratic cost, and\nGaussian disturbances is considered. The system consists of a finite number of\nsubsystems whose dynamics and per-step cost function are coupled through their\nmean-field (empirical average). The system has mean-field sharing information\nstructure, i.e., each controller observes the state of its local subsystem\n(either perfectly or with noise) and the mean-field. It is shown that the\noptimal control law is unique, linear, and identical across all subsystems.\nMoreover, the optimal gains are computed by solving two decoupled Riccati\nequations in the full observation model and by solving an additional filter\nRiccati equation in the noisy observation model. These Riccati equations do not\ndepend on the number of subsystems. It is also shown that the optimal\ndecentralized performance is the same as the optimal centralized performance.\nAn example, motivated by smart grids, is presented to illustrate the result.\n