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Feedback Maximum Principle for Ensemble Control of Local Continuity Equations: An Application to Supervised Machine Learning

Авторы: Staritsyn M., Pogodaev N., Chertovskih R., Pereira F.L.

Журнал: IEEE Control Systems Letters

Том: 6


Год: 2022

Отчётный год: 2022


Местоположение издательства:


Аннотация: 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.

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