Distributed Fixed-time And Prescribed-time Attitude Consensus Control For Multiple Spacecraft Under Directed Graph

Attitude consensus control of multiple spacecraft has become a hot research topic in spacecraft formation flying,which can be applied in the earth observation and deep space exploration.Convergence time is a very fundamental property of the control system and are often used to describe desired specifications and performance requirements for system response.Most of the existing research results are asymptotically stable or finite-time stable.However,the system convergence time is infinite for asymptotic stability.The system convergence time of finite-time control is related to the initial state of the system.When the initial state of the system is far from the equilibrium point,the system convergence time also becomes longer.Fixed-time control and prescribed-time control not only retain the disturbance-rejection characteristics of finite-time control,but also solve the problem that the convergence time of the system depends on the initial state of the system.Fixed-time control can guarantee that the convergence time is just dependent on control parameters.The prescribed-time control uses the convergence time given by the designer to design the control parameters and ensure that the system states converges to the equilibrium within the given time.In many spacecraft formation missions,the spacecraft are required to complete the attitude consensus control within the prescribed time.Therefore,it is of great significance to study the fixed-time and prescribed-time attitude consensus control of multi-spacecraft.Based on the fixed-time and prescribed-time stability theory,this thesis studies the fixed-time and prescribed-time attitudes consensus control problem of multiple spacecraft under the directed communication topology.Based on the above analysis,the main research contents of this thesis are summarized as follows.To solve the problem of distributed fixed-time attitude consensus control of multiple spacecraft under the directed communication topology,a distributed fixed-time leader spacecraft’s attitude observer is designed based on Lyapunov’s fixed-time stability theory and graph theory.Based on the observer,an attitude consensus control law is proposed for the case where the angular velocity of spacecraft can be measured.For the case without the angular velocity measurements,a fixed-time state observer is designed to quickly observe the angular velocity of spacecraft.Then,based on the leader spacecraft’s attitude observer and angular velocity observer,a fixed-time state-feedback attitude consensus control law is proposed.To solve the problem of distributed fixed-time attitude consensus control of multiple spacecraft under input saturation and the directed communication topology,a fixed-time leader spacecraft’s attitude observer is designed,which can estimate the leader spacecraft’s attitude information in a fixed time.Based on the leader spacecraft’s attitude observer,a fixed-time state-feedback attitude tracking controller is designed.For the case without the angular velocity measurements,a fixed-time state observer is designed to estimate the spacecraft angular velocity information within a fixed time.Then,based on the estimated leader spacecraft’s attitude and spacecraft angular velocity information,a fixed-time output-feedback attitude tracking controller is designed.To solve the problem of distributed prescribed-time attitude consensus control of multiple spacecraft under the directed communication topology,a distributed prescribedtime observer is designed to quickly observe the attitude information of the leader spacecraft.Based on the observed attitude information of the leader spacecraft,a prescribedtime attitude consensus control law is proposed.When the input saturation is considered,a new distributed prescribed-time observer is designed to quickly observe the attitude information of the leader spacecraft by using a different method.Then,based on the estimated attitude information of the leader spacecraft,a prescribed-time attitude consensus control law is proposed,where the control torque saturation is considered.To solve the problem of distributed prescribed-time attitude consensus control of multiple spacecraft with the input saturation under the quantization communication and the directed communication topology,a quantization communication strategy is designed to decrease the communication frequency.Then,a designed leader spacecraft’s attitude observer is designed,where the quantization errors are considered.Based on the designed leader spacecraft’s attitude observer,a prescribed-time spacecraft attitude consensus control law is designed.