@article{Liang2026, 
author = {Xiaotian Liang and Yanbo Wang and Lei Yang and Hui Cao and Shuangsi Xue},
title = {Geometric enforcing of sequential convergence in fixed-time stability: An anisotropic vector field approach},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {7},
pages = {21385-21411},
keywords = {sequential convergence, anisotropic vector field, Filippov differential inclusion, affine nonlinear systems, residual reinforcement learning, spacecraft attitude},
url = {https://www.sciopen.com/article/10.3934/math.2026867},
doi = {10.3934/math.2026867},
abstract = {This paper addresses the problem of enforcing a strict temporal sequence on the convergence of state components in affine nonlinear systems. Unlike standard finite-time stabilization, where states converge synchronously or in an arbitrary order, we propose a geometric framework that shapes the phase-space trajectories into a prespecified topological hierarchy. We introduce an anisotropic weighted sign operator that renders the closed-loop system fixed-time stable while imposing an invariant order on the hitting times of the coordinate axes. An explicit nonasymptotic settling-time bound and a sufficient disturbance-rejection condition are derived, and the controller is extended to generic affine nonlinear dynamics via input–output feedback linearization. To accommodate unmodelled perturbations, a projected residual actor–critic policy is added on top of the baseline; we prove via a composite Lyapunov argument that, provided that the residual field is confined within a state-dependent descent cone, both fixed-time stability and sequential ordering are preserved. The framework is validated on a three-dimensional integrator benchmark and on a rigid-body spacecraft attitude case study with a 20% inertia mismatch.}
}