Mixed-Order Nonaffine Strict-Feedback Systems: A FAS Approach Treatment

In this paper, a generalised form of mixed-order nonaffine strict-feedback systems (SFSs) is investigated, and a recursive solution is proposed to convert equivalently the generalised SFS into a high-order fully actuated system (FAS) model. It is shown that, under certain common conditions, the recursive solutions for converting the generalised SFSs into high-order FAS models can be rearranged into direct analytical explicit solutions. Such a high-order FAS approach is more direct and simpler than the first-order system approach since it avoids the process of converting firstly these high-order SFSs into first order ones for stabilization control, and can finally produce a constant linear closed-loop system. Particularly, two special cases of the generalised mixed-order nonaffine SFSs are studied via the proposed FAS approach. Compared with the well-known backstepping method, the proposed FAS approach possesses many merits on control design, such as simplicity, intuition and effectiveness. An numeric example is worked out to demonstrate the effect of the proposed approach.