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

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.