Data-Driven Backstepping Control for a Class of Unknown Nonlinear Strict-Feedback Systems

The tracking control problem for strict-feedback systems with unknown dynamics has been extensively studied. However, most existing control approaches require online approximation models and associated a priori assumptions. In order to avoid the necessity of deriving online models, this article proposes a data-driven backstepping control (DBC) approach for a class of strict-feedback systems with unknown dynamics. First, unlike the widely-studied adaptive backstepping control approaches, we identify the unknown dynamics of each subsystem based on off-line data and develop a data-driven continuous-time Lyapunov equation return controller, ensuring semi-global exponential stability of the error system. Furthermore, we propose a data-driven dynamic surface control (DDSC) approach for the "complexity explosion" problem in DBC. This approach uses a data-driven linear matrix inequality to return the controller, ensuring that the error system remains semi-globally ultimately uniformly bounded, even when the derivative of the virtual controller cannot be calculated. Finally, the superiority and effectiveness of DBC and DDSC are verified by simulation examples.