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Neural Network-Based Distributed Attitude Coordination Control for Spacecraft Formation Flying With Input Saturation An-Min Zou and Krishna Dev Kumar, Senior Member, IEEE Abstract— This brief considers the attitude coordination control problem for spacecraft formation flying when only a subset of the group members has access to the common reference attitude. A quaternion-based distributed attitude coordination control scheme is proposed with consideration of the input saturation and with the aid of the sliding-mode observer, sep- aration principle theorem, Chebyshev neural networks, smooth projection algorithm, and robust control technique. Using graph theory and a Lyapunov-based approach, it is shown that the distributed controller can guarantee the attitude of all spacecraft to converge to a common time-varying reference attitude when the reference attitude is available only to a portion of the group of spacecraft. Numerical simulations are presented to demonstrate the performance of the proposed distributed controller. Index Terms— Attitude coordination control, Chebyshev neural networks, control input saturation, quaternion, spacecraft formation flying. Manuscript received August 2, 2011; revised April 12, 2012; accepted April 20, 2012. Date of publication May 22, 2012; date of current version June 8, 2012. The authors are with the Department of Aerospace Engineering, Ryerson University, Toronto, ON M5B 2K3, Canada (e-mail: anmin.zou@ia.ac.cn; kdkumar@ryerson.ca). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TNNLS.2012.2196710 2162–237X/$31.00 © 2012 IEEE I. I NTRODUCTION Attitude coordination control for spacecraft formation flying (SFF) has received significant attention in recent years. In general, there exist several parameterizations to represent the orientation angles, i.e., the three-parameter representations (e.g., the Euler angles, Gibbs vector, Cayley–Rodrigues parameters, and modified Rodrigues parameters) and the four- parameter representations (e.g., unit quaternion). Using the modified Rodrigues parameters for attitude representations, the problem of attitude coordination has been studied in [1]–[7]. However, the three-parameter representations always exhibit singularity, i.e., the Jacobian matrix in the spacecraft kinematics is singular for some orientations, and it is well known that the four-parameter representations (e.g., unit quaternion) are considered for global representation of orientation angles without singularities. Using unit quaternion for attitude representation, two distributed formation control strategies for maintaining attitude alignment among a group of spacecraft were proposed in [8]. In [9], a decentralized variable structure controller was presented for attitude coordination control of multiple spacecraft in the presence of model uncertainties, external disturbances, and intercommunication time delays. Based on the state-dependent Riccati equation technique, a decentralized attitude coordinated control algorithm for SFF was proposed in [10]. In these works [8]–[10], the common reference attitude was assumed to be a constant. The problem of quaternion- based attitude synchronization for a group of spacecraft to a common time-varying reference attitude was studied in [11]–[14]. However, the common time-varying reference attitude was assumed to be available to each agent in the group. In practice, it is more realistic that a common time-varying reference attitude is available only to a subset of the group members, and it is highly desirable to develop a distributed control law that can force a group of spacecraft to a common time-varying reference attitude even when only a subset of the team members has access to the common reference attitude. In the current literature, attitude coordination control that can be robust against both structured and unstructured uncer- tainties has not received much attention. In [14], a quaternion- based decentralized adaptive sliding-mode control law was proposed for attitude coordination control of SFF in the presence of model uncertainties and external disturbances. However, the common time-varying reference attitude was assumed to be available to each spacecraft in the formation, and the problem of control input saturation was not considered. Universal function approximations such as neural networks (NNs) have been used in the robust control of nonlinear uncertain systems [15]–[19], due to the learning and adaptive abilities of NNs. It is worthwhile mentioning that the NN-based approaches for multiagent systems developed in [17]–[19] cannot be directly applied to spacecraft attitude dynamics because of the inherent nonlinearity in quaternion kinematics. Recently, a pinning impulsive control strategy was proposed for the synchronization of stochastic dynamical networks with nonlinear coupling in [20].