Stabilization of reacting systems

TL;DR

This paper proposes a feedback control method to stabilize reacting Hamiltonian systems by transforming saddle equilibria into stable ones, with applications demonstrated on model Hamiltonians and atomic systems.

Contribution

It introduces a simple, algorithmic feedback stabilization scheme for classical reacting systems and explores destabilization techniques, expanding control strategies in Hamiltonian dynamics.

Findings

Successfully stabilizes saddle equilibria in model systems

Demonstrates stabilization of hydrogen atom in crossed and magnetic fields

Provides a systematic approach for destabilization of stable systems

Abstract

A feedback stabilization scheme to stabilize a classical reacting Hamiltonian system is proposed. It is based on transforming a saddle-type equilibrium to an asymptotically stable one, and is given in a simple and algorithmic way. The question of destabilization of a stable system to make a reacting system is also addressed. The theory is illustrated with the examples of a model Hamiltonian of the form kinetic plus potential, and the hydrogen atom in crossed and magnetic fields.