|Barrier Lyapunov Functions-based Adaptive Control for Nonlinear Purefeedback Systems with Time-varying Full State Constraints
Chunxiao Wang, Yuqiang Wu*, and Jiangbo Yu
International Journal of Control, Automation, and Systems, vol. 15, no. 6, pp.2714-2722, 2017
Abstract : "This paper studies the problem of controller design for pure-feedback nonlinear systems with asymmetric
time-varying full state constraints. The mean value theorem is employed to transform a pure-feedback system into
a strict-feedback structure with non-affine terms. For the transformed system, a time-varying asymmetric Barrier
Lyapunov Function (ABLF) with the error variables is employed to ensure the time-varying constraints satisfaction.
By allowing the barriers to vary with the desired trajectory in time, the initial condition requirements are relaxed
efficiently. The presented control scheme can guarantee that all signals in the closed-loop system are ultimately
bounded. It is also proved that the tracking error converges to an adjustable neighborhood of the origin even in the
presence of disturbance. The performance of the ABLF-based control are illustrated through two examples."
ABLF, backstepping, full state constraints, nonlinear pure-feedback system, time-varying.