Low-complexity control design for uncertain pure-feedback systems subject to state and tracking error constraints

In this work, a low-complexity technique is developed to design controller for uncertain pure-feedback systems, which may be subject to time-varying yet asymmetric state and tracking error constraints simultaneously. By directly incorporating the state and tracking error constraint functions into the control design, a control scheme is proposed without utilizing any nonlinear approximator as well as any priori knowledge of system nonlinearities. A novel Lyapunov analytical method is structured for its stability analysis and it is shown that all the signals in the closed-loop system are guaranteed to be bounded and the state and tracking error constraints are never violated. With certain prescribed tracking performance specifications, the range of the constraints imposed on the states should be large enough, and there is a trade-off between tracking performance and the flexibility of the admissible state constraints. Besides, the "explosion of complexity" issue of backstepping and the feasibility conditions on virtual controllers are totally avoided. The effectiveness and flexibility of such methodology is demonstrated by a single-link robot dynamics.