Addressing complex state constraints in the integral barrier Lyapunov function-based adaptive tracking control

For the state-constrained control problem with complex constrained regions, this paper presents an Integral Barrier Lyapunov Function-based adaptive backstepping scheme for the tracking control. The Barrier Lyapunov Function approach provides an effective tool to embed the barrier terms into the Lyapunov function, enabling the integration of barrier avoidance and closed-loop stabilisation. In the literature, previous works in the area of Barrier Lyapunov Function mostly considered a simple hyperrectangle shape of the constrained region. In this study, the complex barrier region is for the first time introduced to the Barrier Lyapunov Function framework. A novel recursive design procedure is constructed for a class of uncertain nonlinear parametric systems, ensuring the closed-loop signals are all bounded and the tracking errors are convergent. Finally, the proposed method is applied to a numerical example, illustrating the efficacy of this work.