In this paper, on–off SDRE control approach is presented for spacecraft formation flying control around sun-earth L2 libration point. Orbits around libration points are significant targets for many space missions mainly because of efficient fuel consumption. Furthermore, less propellant usage can be achieved by considering optimal control approaches in spacecraft formation flying control design. Among various nonlinear and optimal control methods, SDRE has shown to be a popular controller in various missions due to the privileges including efficiency, accuracy and robustness. The spacecraft are assumed to have on–off thrusters as actuators. It requires them to be fed with a sequence of on–off pulses which is regarded as a challenge for spacecraft designers. Hence, the main contribution of this paper is designing an on–off SDRE approach for the formation flight around sun-earth L2 point with uncertainty with energy and accuracy considerations. Including on–off input as a constraint is not feasible for SDRE implementation because it makes the system non-affine. An alternative is utilizing an integral action technique and an auxiliary control to make the system affine which leads to on–off SDRE approach. It has also been shown that the proposed method is robust against parametric uncertainties of the states. Present study aims to design an energy-beneficial, simple and attractive controller for a complex nonlinear system with on–off inputs and uncertainty in CRTBP. Simulation results show that the on–off SDRE control could provide the formation flight around L2 point with high accuracy using less energy consumption.

在本文中，提出了在太阳地球L2释放点附近控制航天器编队飞行的开-关SDRE控制方法。解放点周围的轨道是许多太空任务的重要目标，主要是因为有效的燃料消耗。此外，通过在航天器编队飞行控制设计中考虑最佳控制方法，可以减少使用推进剂。在各种非线性和最佳控制方法中，由于具有效率，准确性和鲁棒性等特权，SDRE在各种任务中已成为受欢迎的控制器。假定该航天器具有开关推进器作为执行器。它要求给他们提供一系列的开关脉冲，这对航天器设计者来说是一个挑战。因此，本文的主要贡献是设计了一种开-关SDRE方法，用于绕着地球L2点的编队飞行，其中考虑了能量和精度方面的不确定性。将开-关输入作为约束对于SDRE实施是不可行的，因为这会使系统变得非仿射。一种替代方法是利用积分作用技术和辅助控制使系统仿射，从而导致采用开-关SDRE方法。还已经表明，所提出的方法对于状态的参数不确定性是鲁棒的。目前的研究旨在为具有开/关输入和CRTBP不确定性的复杂非线性系统设计一种节能，简单且有吸引力的控制器。