Schrodinger Approach to Optimal Control of Large-Size Populations

• 成果类型: Article
• 署名作者: Bakshi, Kaivalya; Fan, David D.; Theodorou, Evangelos A.
• 署名单位: University System of Georgia; Georgia Institute of Technology; University System of Georgia; Georgia Institute of Technology
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.3007543
• 发表日期: 2021
• 页码: 2372-2378
• 关键词: Sociology; statistics; stability analysis; optimal control; Mathematical model; Stochastic processes; Transforms

摘要

Large-size populations consisting of a continuum of identical and noncooperative agents with stochastic dynamics are useful in modeling various biological and engineered systems. This article addresses the stochastic control problem of designing optimal state-feedback controllers that guarantee the closed-loop stability of the stationary density of such agents with nonlinear Langevin dynamics, under the action of their individual steady-state controls. We represent the corresponding coupled forward-backward partial differential equations as decoupled Schrodinger equations, by applying two variable transforms. Spectral properties of the linear Schrodinger operator that underlie the stability analysis are used to obtain explicit control design constraints. Our interpretation of the Schrodinger potential as the cost function of a closely related optimal control problem motivates a quadrature based algorithm to compute the finite-time optimal control.