Towards a Generic Constructive Nonlinear Control Design Tool using Relaxed Control

In this technical note, we revisit a control design approach for general (non-affine) nonlinear systems using relaxed control. Using the notion of relaxed input, where the ordinary real-valued control input is replaced by a measure-valued control input, we are able to manipulate the original system such that the resulting relaxed system is amenable to control. We show the applicability of using relaxed input for transforming a non-affine nonlinear system into an affine one such that the relaxed system has desirable control properties. Finally, we present a practical implementation of relaxed input via ordinary control input which is based on the sampled-data of the relaxed input.