Diffeomorphism-based control of nonlinear systems subject to state constraints with actual applications

This paper briefly collect the results of a more general approach of control of nonlinear systems with state-&-input constraints, recently proposed by some of the authors in [1]. In that work we provide some insights and tools for the constrained state control problem with Barrier Lyapunov Functions. Here we provide a different and constructive outlook which allows to transform the constrained-state control problem into a Lyapunov-based control design on an unconstrained dynamics. Moreover, it is shown that the problem can also be solved for non-structured nonlinear systems. Surprisingly only some foundations of differential geometry and two extra assumptions were needed to construct a tool based on the well-established theories of control Lyapunov functions and Sontag´s universal formula. Simple examples and a real application of dynamic positioning for ships with nonlinear position constraints are provided. The latter has been tested in a real scenario with a realistic simulator owned by shipbuilding company [2]. Some results are shown in a companion work [9].