Robotics, mechatronics and autonomous systems can exhibit complex nonlinear dynamics which can lead to unsatisfactory transients and deviation from setpoints or even to instability. A standard approach in the control of these systems had been the concept of diffeomorphisms to bring a system into a linear form. However, these methods are not straightforward and result in complicated state-space model transformations. In this monograph, new methods have been investigated which are not constrained by the shortcomings of global linearization-based control schemes. They can be implemented in a computationally simple manner, are followed by global stability proofs, and perform better than previous optimal control approaches for a wider class of nonlinear dynamical systems and applications.