부산대학교 도서관

We study the problem of designing optimal parameter-invariant control for an ensemble of structurally similar ODEs. The statistical behavior of the ensemble is characterized by the mean-field, transported in the space of probability measures. The optimization problem has a linear-quadratic structure: the dynamics given by the continuity equation are linear in the state-measure, and the cost is quadratic since the integrand is along the square of the measure. To solve this problem, we design a conceptual iterative method that operates with ensemble controls of the measure-feedback form. We point out several numerical aspects of the implementation of this optimization method, and demonstrate its modus operandi by treating a simple model from mathematical neuroscience. Our approach involves an exact representation of the increment of the objective functional. Formal arguments behind this representation are surprisingly simple, since they do not appeal to advanced analysis in the space of probability measures, and can be extended to a broader class of extremal problems of a similar form.