Second-Order Nonaffine SFSs: A FAS Approach Treatment

This paper investigates the synthesis problem of a class of generalized nonaffine second-order strict-feedback systems (SFSs) by using the fully-actuated system (FAS) approach. The generalized system under consideration permits each state equation to exhibit nonlinear dependence on the next state variables, while also allowing the control input to be nonlinearly embedded within the system dynamics. In contrast to the conventional state-space approach, under certain common conditions, a recursive design framework is developed to convert equivalently generalized nonaffine second-order SFSs into a high-order fully actuated (HOFA) model by employing the principle of “ascending order and descending dimension”. Subsequently, leveraging the theory of FAS, controllers can be directly designed for such high-order system, resulting in a constant linear closed-loop system. This approach eliminates the need to convert second-order SFSs into first-order state-space form, thereby offering a more straightforward and concise methods. Moreover, it effectively avoids the differentiation explosion problem commonly encountered in classical backstepping techniques. A numerical simulation is provided to show the effect of the control scheme.