학술논문
Feedback Maximum Principle for Ensemble Control of Local Continuity Equations: An Application to Supervised Machine Learning
Document Type
Periodical
Source
IEEE Control Systems Letters IEEE Control Syst. Lett. Control Systems Letters, IEEE. 6:1046-1051 2022
Subject
Language
ISSN
2475-1456
Abstract
We consider an optimal control problem for a system of local continuity equations on a space of probability measures. Such systems can be viewed as macroscopic models of ensembles of non-interacting particles or homotypic individuals, representing several different “populations”. For the stated problem, we propose a necessary conditions of optimality which involve feedback controls inherent to the extremal structure designed via the standard Pontryagin’s Maximum Principle. These optimality conditions admit a realization as an iterative algorithm for optimal control. As a motivating case, we discuss an application of the derived optimality condition, and the consequent numeric method to a problem of supervised machine learning via dynamic systems.