Optimal prescribed-time attitude tracking for multiple spacecraft systems based on adaptive critic algorithm

In this paper, an adaptive critic-based approximate optimal control scheme is constructed for the attitude coordinated tracking problem with prescribed performance requirements and input saturation constraint. Since the virtual leader’s information is not available for some followers, a predetermined-time distributed observer is deployed for each follower to reconstruct the leader’s information. Subsequently, an error transformation procedure is imported to reformulate the prescribed-time attitude coordination issue with prescribed performance constraint as the stabilization one of an unconstraint error system. To confront the input saturation constraint, a nonquadratic function is included in the cost function and in this case the described issue is formulated as a series of nonlinear optimal control problems. The critic architecture is built to approximately solve the corresponding Hamilton-Jacobi-Bellman (HJB) equation, i.e., only critic neural network (NN) is utilized to reconstruct the value function and control policy for each follower. The effectiveness and advantage is validated through numerical examples.