Prescribed finite-time boundary control of constrained flexible satellite systems with translational motion modeling

Abstract

This study presents an adaptive prescribed finite-time boundary control approach for a flexible satellite system with full-state constraints. The system is represented mathematically by partial differential equations with boundary conditions, and a prescribed finite-time boundary control algorithm is developed through backstepping to suppress center-body vibrations. The Nussbaum function is used to address the nonlinear effects caused by input saturation. A suitable barrier Lyapunov function is constructed to demonstrate that the center-body displacement and velocity remain within the prescribed constraint domain for a predetermined time regardless of their initial values. Additionally, the suggested approach ensures that the system's state variables remain within their allowable ranges and that the closed-loop system signals do not exceed their specified bounds. Simulations are carried out and the outcomes show how effective the suggested strategy is.