Optimized Backstepping Attitude Containment Control for Multiple Spacecrafts

This article investigates the attitude containment control problem for multiple spacecrafts based on optimized backstepping design strategy. First, the spacecrafts' attitude dynamics are modeled by modified Rodrigues parameters and are rewritten in the strict-feedback form. Then, we incorporate the idea of optimal control into each step of backstepping design procedure. At each step, the optimal virtual/actual control law is obtained via actor-critic reinforcement learning algorithm and approximated by fuzzy logic systems (FLSs). The updating laws of the parameter matrices are designed in a more concise form and the persistent excitation condition is relaxed. According to the Lyapunov stability analysis, the containment error and FLS parameter errors are semiglobally uniformly ultimately bounded. Finally, a simulation example is given to illustrate the effectiveness of the proposed method.