Simplification of dynamic problems by time-scale transformation: application to the nonlinear control with input positive constraints

In this paper, we show how time-scale transformations (TST) can be used for the control of nonlinear sytems subject to positive constraints. Such transformations, which consist in a change of the time variable, enable to define a new time-scale denoted τ in which the control problem becomes unconstrained and is therefore simplified. Classical methods such as dynamic feedback linearizing control design can then be used, leading to control laws that naturally fullfill the input positive constraints. The proposed method is applied on two concrete examples and compared with an other approach