Adiabatic feedback control of Hamiltonian systems

TL;DR

This paper introduces an adiabatic feedback control method for classical Hamiltonian systems, enabling energy manipulation and state control through adiabatic invariants, with applications demonstrated on nonlinear physics models.

Contribution

It develops a novel control framework using adiabatic invariants for Hamiltonian systems, extending control capabilities to heating, cooling, and trapping.

Findings

New adiabatic invariant for control

Mechanisms for heating and cooling identified

Control of many-body systems via single coordinates

Abstract

We study feedback control of classical Hamiltonian systems with the controlling parameter varying slowly in time. The control aims to change system's energy. We show that the control problems can be solved with help of an adiabatic invariant that generalizes the conservation of the phase-space volume to control situations. New mechanisms of control for achieving heating, cooling, entropy reduction and particle trapping are found. The feedback control of a many-body system via one of its coordinates is discussed. The results are illustrated by two basic models of non-linear physics.