Adaptive Barrier-Lyapunov-Functions Based Control Scheme of Nonlinear Pure-Feedback Systems with Full State Constraints and Asymptotic Tracking Performance

In this paper, the authors propose an adaptive Barrier-Lyapunov-Functions (BLFs) based control scheme for nonlinear pure-feedback systems with full state constraints. Due to the coexist of the non-affine structure and full state constraints, it is very difficult to construct a desired controller for the considered system. According to the mean value theorem, the authors transform the pure-feedback system into a system with strict-feedback structure, so that the well-known backstepping method can be applied. Then, in the backstepping design process, the BLFs are employed to avoid the violation of the state constraints, and neural networks (NNs) are directly used to online approximate the unknown packaged nonlinear terms. The presented controller ensures that all the signals in the closed-loop system are bounded and the tracking error asymptotically converges to zero. Meanwhile, it is shown that the constraint requirement on the system will not be violated during the operation. Finally, two simulation examples are provided to show the effectiveness of the proposed control scheme.