Time-varying IBLFs-based adaptive control of uncertain nonlinear systems with full state constraints

This paper presents an adaptive control design for nonlinear systems with time-varying full state constraints. It is the first time to introduce the novel time-varying Integral Barrier Lyapunov functions (TVIBLFs) into the adaptive control design, which not only overcomes the limitation of conservatism existing in the traditional BLFs, but also guarantees that the full state time-varying constraint bounds are not violated. The TVIBLFs are combined with the backstepping design procedure to construct the controllers and adaptation laws, and the integral mean value theorem is used to differentiate TVIBLFs. It can be proven that all the states are forced in the time-varying regions and the stability of the closed-loop system is achieved. The effectiveness of the proposed adaptive control strategy can be illustrated through a simulation example.