State-dependent event-triggered fractional-order control with prescribed performance for free-floating space manipulators

Free-floating space manipulators (FFSMs) usually operate in complex situations that impose stringent performance requirements while offering only limited communication resources. To address these challenges, this paper proposes a Lorentz-function-based state-dependent event-triggered fractional-order sliding mode controller (SMC) with a shear-mapping prescribed performance transformation. Different from traditional prescribed performance control (PPC), which requires the initial tracking error to satisfy the prescribed boundary, the proposed shear mapping transformation relaxes the initial feasibility condition and avoids transformation singularity under bounded initial or transient boundary violations. Meanwhile, the proposed controller drives the tracking errors into the prescribed performance envelope and achieves predefined-time convergence independent of initial system states. In addition, by incorporating the Lorentz function into a relative-threshold mechanism, a state-dependent event-triggered condition is developed to adaptively regulate triggering intervals according to deviations in the system states, thereby reducing communication frequency. Theoretical analysis proves the closed-loop stability and the exclusion of Zeno behavior. Simulation results show that all tracking errors converge within the predefined time in both joint- and task-space operations, while the aggregate number of control updates is reduced by 19.36% compared with the traditional event-triggered scheme.