Control of ordinary differential equations using Bagarello's operator approach : Case of forced harmonic oscillator systems

TL;DR

This paper applies Bagarello's operator approach combined with Pontryagin's maximum principle to control nonlinear differential equations, exemplified by forced harmonic oscillator systems, providing a series expansion solution involving commutators.

Contribution

It introduces a novel method integrating Bagarello's operator approach with optimal control theory for nonlinear differential systems.

Findings

Series expansion solutions for controlled systems

Application to forced harmonic oscillator systems

Demonstration of the method's effectiveness

Abstract

This work deals with the study of an optimal control of a system of nonlinear differential equations using the Bagarello's operator approach, recently introduced in a paper (Int. Jour. of Theoretical Physics, 43, issue 12 (2004), p. 2371 - 2394). The control problem is reduced by using the Pontryagin's maximum principle, to a system of ordinary differential equations with unknown state and adjoint variables. Its solution is then described in terms of a series expansion of commutators involving an unbounded self-adjoint, densely defined, system Hamiltonian operator H and initial position operators. Relevant simple applications are discussed.