Predefined-time optimal control for 6-DOF air-bearing testbed formation system: learning enhancement and disturbance compensation

The six-degree-of freedom (6-DOF) air-bearing testbed (ABT) functions as a terrestrial ground simulator of spacecraft dynamics, exhibiting significant nonlinear characteristics. This paper proposes a predefined-time optimal learning control strategy tailored for 6-DOF ABT formation system, proficiently handling lumped disturbances under switching digraphs. A predefined-time extended state observer is initially formulated to forecast essential leader state information under heterogeneous communication delays, while effectively alleviating the boundedness requirements on lumped disturbances and their derivatives. Subsequently, a novel predefined-time optimal learning distribution controller is proposed utilizing adaptive dynamic programming techniques, delivering near-optimal tracking control performance. Notably, this methodology uniquely integrates a learning-based online weight update mechanism, substantially amplifying learning capabilities of neural networks through efficient sample data extraction and filtration, thereby facilitating the optimization of control performance. The global stability is rigorously demonstrated through Lyapunov theory. Comprehensive numerical simulations alongside practical ground experiments further validate the superiority and engineering applicability of proposed findings.