Simplified Optimal Backstepping Control for a Spacecraft Based on Flexible Prescribed Performance with Non-Initial Constraint

This paper addresses the position and attitude control of combined spacecraft in on-orbit servicing missions, taking into account model parameter uncertainties, unknown external disturbances, and fuel-optimal constraints. A novel flexible prescribed-performance optimal backstepping controller without initial constraints is proposed by incorporating an Actor-Critic-Identify neural network architecture. First, a dynamic model of the combined spacecraft is established, with all uncertainties treated as lumped disturbances. To improve transient performance and remove initial value constraints, a flexible prescribed performance function is designed, which accommodates input saturation and decouples settling time from both initial states and controller parameters. Subsequently, a steady-state performance optimized Identify weight adaptation law is employed for rapid and accurate estimation of the nonlinear lumped disturbances. For fuel optimization, a simplified Actor-Critic adaptation law is developed, eliminating the need for complex step-by-step derivations while ensuring weight convergence. The uniform ultimate boundedness of the closed-loop system is proven using Lyapunov theory. Numerical simulations and semi-physical experiments verify the proposed method’s advantages in both steady-state and transient performance, as well as its applicability to on-orbit implementation.