Robust Prescribed-time Consensus With Actuator Saturation

The research on consensus algorithm of multi-agent sytems has been originated from the fact that single-agent system can not satisfy growing needs in actual problems.Especially when the era of artificial intelligence comes,it becomes especially important for multiple simple agents to cooperate with each other to complete more complex tasks.With the development of basic subjects such as mathematics and computer science,the consensus algorithm of multi-agents systems has also made great progress.In order to improve previous centralized control method,distributed consensus algorithm was proposed.It uses only local information and exchanges data with neighbor nodes without the coordination of a central node,and still can force the multi-agent systems reach consensus.The key of the distributed consensus algorithm is to design suitable control protocols for each agent to force the multi-agent systems to reach the same states.Stability and accuracy are the basis index for every control algorithm.On rapidity,to make the multi-agent systems reach consensus faster,finite-time consensus algorithm and fixed-time consensus algorithm are proposed.They force the multi-agent systems reach consensus faster but need larger input.Most actual systems can’t provide so much energy so saturation problem is also worthy of attention.What’s more,to make the control protocols better used in acutal systems,robustness is a hot point that researchers pay attention to.Therefore,focusing on the above problems,this thesis considers rapidity,robustness and saturation problems in distributed consensus algorithm.The main contributions are summarized as follows:(1)For leader-following multi-agent systems,to improve robustness in consensus algorithm,this thesis firstly proposes a prescribed-time disturbance and actuator faults observer.With the proposed observer,the sum of the disturbance and actuator faults can be tracked in prescribed-time.Then,a distributed prescribed-time state observer is proposed in this thesis.Leader agent’s state can be observed by the distributed state observer and send to every follower agent in prescribed-time.Moreover,the prescribed time can be set in advance and offline.(2)A prescribed-time consensus control algorithm is designed in this thesis for a kind of leaderfollowing multi-agent systems.The proposed algorithm can force the multi-agent systems reach consensus in prescribed time with uncertain disturbance and actuator faults.Considering saturation problems,a maximum control input is limited in the proposed algorithm.When saturation occurs,the whole system can still meet design requirements.Besides,a method to figure out the lower bound of the prescribed time is proposed.As well,the prescribed time can be set in advance and offline.(3)When designing prescribed-time consensus algorithm,jumping variation problem is found to appear near the prescribed time point sometimes.To solve this problem,this thesis proposes leadtime consensus algorithm of multi-agent systems,which makes the jumping variation disappear and presents greater curve.By using the proposed algorithm,the leader-folloing multi-agent systems can reach consensus in lead time and the saturation problem is settled.As well,the lead time can be set in advance and offline without knowing initial sates.