Finite-Time Attitude Synchronisation Control Design For Multiple Spacecraft Systems

Attitude synchronisation control is an important research content of multiple spacecraft formation ?ying, and it plays a signi?cant role in many actual formation tasks, e.g.,synthetic aperture imaging, space-based synthetic aperture radar interferometry, etc., thus it has received the researchers’ extensive concern in recent decades. The dynamic model of spacecraft is nonlinear, and it is subject to inertia uncertainties, unknown time-varying disturbance, actuator faults, etc., which will have a negative impact on the control accuracy, coordination capability and even the stability of the multiple spacecraft systems.With the structure and tasks being more and more complex and diversi?ed, the traditional control scheme is obviously di?cult to meet the multi-performance requirements of attitude control for multiple spacecraft systems. Based on the sliding mode control and adaptive mechanism, this thesis will investigate the ?nite-time attitude synchronisation control problem for multiple spacecraft systems in various conditions. The main content of this thesis can be summarized as follows:1. The problem of ?nite-time attitude synchronisation for multiple spacecraft is discussed in the presence of unknown time-varying disturbances. Based on the graph theory,adaptive mechanism, switching surface-based nonsingular fast terminal sliding manifold and ?nite-time control technique, a decentralised ?nite-time attitude synchronisation control scheme is designed based on the undirected graph, and the rigorous stability proof is presented. Simulation examples are provided by using a group of four spacecraft, simulation results demonstrate the correctness and e?ectiveness of the algorithm.2. The ?nite-time attitude synchronisation control problem for multiple spacecraft is investigated under directed topology. First of all, a decentralised nonsingular fast terminal sliding mode is designed based on the graph theory. Considering the in?uence of unknown time-varying disturbances and combining the adaptive control mechanism, a ?nite-time attitude synchronisation control scheme is developed, in which no priori information about the upper bounds of the disturbances is required, and the ?nite-time convergence of the tracking errors and relative errors can be guaranteed in small regions. Finally, two simulation examples are provided to illustrate the feasibility and superiority of the algorithm, and through comparative analysis, we present the general rules about how the related design parameters in?uence the control performances.3. After that, considering the in?uence of inertia uncertainties and unknown timevarying disturbances simultaneously, the problem of attitude synchronisation under directed topology is discussed. Based on the graph theory, adaptive mechanism and nonsingular fast terminal sliding mode control technique, a decentralised ?nite-time attitude synchronisation control scheme is designed, and the ?nite-time convergence of the attitude tracking errors is proved rigorously, furthermore, the explicit expression of small regions bounds are calculated. The proposed algorithm requires no priori accurate information on inertia uncertainties and disturbances, and can provide strong robustness against spacecraft inertia uncertainties and external disturbances, together with faster convergence and higher precision.4. In the presence of inertia uncertainties and unknown time-varying disturbances,the problem of distributed ?nite-time attitude synchronisation for multiple spacecraft with a dynamic virtual leader is investigated. The virtual leader gives commands to some of the follower spacecraft, and the communication network between followers can be an undirected or a directed graph. First of all, by using two neighborhood synchronisation error signals, a ?nite-time cooperative control algorithm is designed associated with adaptive mechanism. Furthermore, without relying on the neighboring accurate states information,another distributed ?nite-time cooperative control algorithm is developed by using the followers’ estimates of the virtual leader. Both of the control strategies can guarantee all the follower spacecraft synchronise to the virtual leader in ?nite time. Applying the continuous design, both of the algorithm are chattering-free, furthermore, they can provide excellent performances, i.e., strong robustness, high accuracy and fast response.5. Based on the investigation above, we further study the problem of distributed?nite-time attitude synchronisation for multiple spacecraft in the presence of modeling uncertainties, external disturbances and actuator faults. When the communication ?ow between followers is directed, two distributed ?nite-time fault-tolerant control algorithms are designed by employing the neighborhood synchronisation error signals and the followers’ estimates of the virtual leader, respectively. Both of the control schemes can guarantee the?nite-time convergence of the attitude errors and angular velocity errors successfully. In particular, the two algorithms do not require online identi?cation of the actuator faults,and can provide the properties of fault-tolerant, high control precision, fast convergence,strong robustness and chattering attenuation.In the end, we summary up the main results in this thesis and the prospects for future work.