A characterization of cone nonnegativity of Moore–Penrose inverses of unbounded Gram operators

Cooperative braking of urban rail vehicles with Koopman model predictive control

“…where X lift_i denotes the current dataset, X + lift_i denotes the next time dataset, and † denotes the Moore-Penrose pseudo-inverse of a matrix [25].…”

“…Then, the analytical solutions to (21) and (22) can be obtained, $$$$\begin{equation} {\left[ {A_i,B_i} \right]} = {{\bf X}}_{{{\bf lift\_i}}}^{ {\bf +} }{{\left[ {{{{\bf X}}_{{{\bf lift\_i}}}},{{\bf U_i}}} \right]}^\dag }, \end{equation}$$$$ $$$$\begin{equation} C_i = {{\bf X_i}{\bf X}}_{{{\bf lift\_i}}}^\dag , \end{equation}$$$$where $${{\bf X}}_{{\bf lift\_i}}$$ denotes the current dataset, $${{\bf X}}_{{{\bf lift\_i}}}^{ {\bf +} }$$ denotes the next time dataset, and † denotes the Moore–Penrose pseudo‐inverse of a matrix [25].…”