First-Order Nonaffine SFSs: A FAS Approach Treatment

In this paper, we proposed a novel scheme to deal with nonaffine strict-feedback systems (SFSs) by using fully actuated system (FAS) approach. The proposed scheme involves a recursive solution that introduces an intermediate function, derives its inverse, and then equivalently transforms the nonaffine SFS into a FAS model. Furthermore, it is shown that under certain special cases where the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$i$</tex>-th control vector function depends only on the (<tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$i+1$</tex>) -th state, two simplified solutions are provided. The first directly transforms the nonaffine SFS into a FAS model using recursive solutions, while the second first converts the nonaffine SFS into an affine SFS and then utilizes existing results to transform the affine SFS into a FAS model. In another special case, where the nonlinear terms vanish, the nonaffine SFS can be reexpressed as the well-known pseudo pure-feedback system, and a corresponding transformation into a FAS model is also provided. By transforming the original system into a FAS model, the FAS approach enables direct control law design, offering a more effective alternative to the well-known backstepping method while avoiding the “explosion of complexity” problem inherent in backstepping. The theoretical results are validated through simulation tests.