Optimal control problem governed by an infinite dimensional two-nilpotent bilinear systems

Abstract

<p style='text-indent:20px;'>The object of this work is to construct an explicit linear operators <inline-formula><tex-math id="M1">\begin{document}$ A $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M2">\begin{document}$ B $\end{document}</tex-math></inline-formula> which generate a nilpotent Lie algebra for the bracket <inline-formula><tex-math id="M3">\begin{document}$ \left[A,B\right] = AB-BA $\end{document}</tex-math></inline-formula> of degree 2 in infinite dimensional spaces. This construction can be applied to give an exact optimal solution for a class of infinite dimensional bilinear systems.</p>