Flexible Performance Control Under Constrained Actuation for Nonsquare Nonlinear Systems With Controllability Relaxation.

Prescribed performance control (PPC) for nonsquare nonlinear systems with unknown time-varying control gains and actuator constraints remains largely unexplored. This article addresses this problem by integrating a relaxed controllability condition with a flexible performance control framework based on saturation deficiency. Specifically, a refined matrix decomposition and transformation are employed to relax the controllability conditions for uncertain nonsquare nonlinear systems. Subsequently, the original system is augmented with constructed saturation auxiliary systems, which not only alleviate the effects of nonsmooth saturated inputs but also facilitate the backstepping control design under actuator saturation. To balance actuator constraints and performance requirements, we design a tunnel-shaped prescribed-time performance function (PTPF) equipped with saturation awareness capability. This function flexibly extends the performance boundaries during saturation, ensuring that the tracking error remains within the prescribed constraints while placing no restrictions on the saturation level. Both theoretical analysis and over-actuated spacecraft simulations confirm the proposed strategy's capability to achieve flexible prescribed tracking performance under actuator constraints.