Fully actuated system approach for stabilization control of sub-strict feedback systems

This paper proposes a substabilization control method for a class of strict feedback systems with singular value gain functions based on Fully Actuated System (FAS) approach. Firstly, the definition of sub-Strict Feedback System (sub-SFS), including the feasible set and singular set of this system, is given. Then, it is revealed that the sub-SFS can be transformed into a sub-FAS with high order by model transformation under certain conditions, and the corresponding attraction region is described precisely based on the concepts of substability and substabilization of FAS. Furthermore, by using the control characteristics of FAS, the stabilization control law of the sub-SFS can be explicitly solved in a very simple way, and the linear constant closed-loop control system is obtained. The proposed approach not only greatly reduces the design complexity, but also effectively avoids the controller singularity problem by using the feasibility conditions. Finally, theoretical stability analysis and numerical simulation are conducted to illustrate the effectiveness of the proposed approach.