Optimal Control of Spacecraft Formation With Predefined Performance via Extended State Method

This paper investigates the optimal control problem for spacecraft formation with predefined performance by proposing a sliding mode controller based on the State-Dependent Riccati Equation (SDRE) method. First, a controller with an adjustable variable is designed using sliding mode control theory, aimed at minimizing formation error, reducing energy consumption, and optimizing the convergence process of the sliding surface. To manage the predefined performance constraints, a nonlinear function related to these constraints is directly incorporated into the controller and optimal performance index function, simplifying the computations involved. Next, the sliding surface is introduced into the system equations as an extended state to enhance the system's disturbance rejection capability. The adjustable variables on the sliding surface are obtained by applying the SDRE method. Finally, simulations demonstrate that the controller effectively achieves optimal control of spacecraft formation while meeting the predefined performance criteria.