Schrödinger Approach to Optimal Control of Large-Size Populations

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