Stabilization for an ensemble of half-spin systems

• Grant number: 11/03403-3
• Support Opportunities: Scholarships abroad - Research
• Start date: June 27, 2011
• End date: July 13, 2011
• Field of knowledge: Engineering - Electrical Engineering - Industrial Electronics, Electronic Systems and Controls
• Principal Investigator: Paulo Sergio Pereira da Silva
• Grantee: Paulo Sergio Pereira da Silva
• Host Investigator: Pierre Rouchon
• Host Institution: Escola Politécnica (EP). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Institution abroad: ParisTech, France

Abstract

Half spin systems are modelled by Bloch equations. When such systems are immersed in a magnetic field, and they are subject to the Larmor dispersion, the corresponding dynamic behavior is dictated by an infinite number of Bloch equations that parameterized by a angular frequence $\omega$. Such "Ensemble" of systems possesses a common input (u,v)$. The problem of controlling the entire ensemble only using the commom pair of inputs is a hard problem in Quantun Control Theory. Only some restrict results are available in the present literature. A version of this problem was considered in a previous research, where we have obtained some local stability results. The aim of this research is to consider a generalization of this problem towards global stabilization of the Ensemble. The approach is an extension of LaSalle invariance in an infinite dimensional context. Here the state space is the Sobolev space H1 and the Lyapunov function is inspired on the square of H1 norm. (AU)