Barrier Integral Control for Global Asymptotic Stabilization of Uncertain Nonlinear Systems under Smooth Feedback and Transient Constraints
<|reference_start|>Barrier Integral Control for Global Asymptotic Stabilization of Uncertain Nonlinear Systems under Smooth Feedback and Transient Constraints: This paper addresses the problem of asymptotic stabilization for high-order control-affine MIMO nonlinear systems with unknown dynamic terms. We introduce Barrier Integral Control, a novel algorithm designed to confine the system's state within a predefined funnel, ensuring adherence to prescribed transient constraints, and asymptotically drive it to zero from any initial condition. The algorithm leverages the innovative integration of a reciprocal barrier function and an error-integral term, featuring smooth feedback control. Notably, it operates without relying on any information or approximation schemes for the (unknown) dynamic terms, which, unlike a large class of previous works, are not assumed to be bounded or to comply with globally Lipschitz/growth conditions. Additionally, the system's trajectory and asymptotic performance are decoupled from the uncertain model, control-gain selection, and initial conditions. Finally, comparative simulation studies validate the effectiveness of the proposed algorithm.<|reference_end|>
@article{verginis2024barrier,
    title={Barrier Integral Control for Global Asymptotic Stabilization of
  Uncertain Nonlinear Systems under Smooth Feedback and Transient Constraints},
    author={Christos K. Verginis},
    journal={arXiv preprint arXiv:2409.04767},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.04767},
    primaryClass={eess.SY cs.SY}
}