2020/12/04 by Jalal Arabneydi, Arabneydi, Jalal, Aditya Mahajan +1
Economics, Econometrics and Finance · Engineering · Mathematics · #FOS: Mathematics #Mathematical Biology Tumor Growth #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2012.02401
openalex publication_date 2020/12/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we investigate team optimal control of coupled major-minor subsystems with mean-field sharing. In such a model, there is one major subsystem that directly influences the dynamics of n homogeneous minor subsystems; however, the minor subsystems influence the dynamics of the major subsystem and each other only through their mean behaviour (indirectly). In this model, the major and the minor subsystems are arbitrarily coupled in the cost and have mean-field sharing information structure. We propose a two-step approach. In the first step, we describe a mean-field sharing model with multiple types of minor subsystems as a generalization of the mean-field sharing model of Arabneydi and Mahajan, CDC 2014. In the second step, we use the results obtained in the first step to construct a dynamic programming decomposition to identify optimal strategies for the major and the minor subsystems. We present an example with numerical results to illustrate the approach.