On the Optimization and Global Linearization of Nonlinear Systems

The optimization and global linearization of nonlinear mechanical systems are studied in this paper. For a specific but rather general cost function, two theorems are proven which show that the optimization with respect to the control vector, or the acceleration vector, or the transformed new control vector are equivalent. Consequently, it is possible to linearize the nonlinear systems first and then optimize the obtained linear systems, this will give the same results to that obtained by optimizing the nonlinear systems directly.