Formation-containment Control Of Multi-agent Euler-lagrange Systems With Constraints

The multi-agent cooperative system with strong robustness,high reliability and high safety is an important guarantee for the future multi-agent cooperative control theory to be successfully applied in engineering practices.However,most of the existing multi-agent cooperative control algorithms cannot meet the requirements of many practical engineer-ing tasks.This dissertation studies the formation-containment control problem,in which the leader-follower working pattern can meet the needs of many engineering tasks.Un-der some certain conditions,formation-containment control problem can be transformed into various basic cooperative control problems.Different from the previous studied formation-containment control with decentralized working pattern,this dessertation pro-poses distributed working pattern for the formation-containment control.On the other hand,to better apply the theoretical results to the engineering practices,many practical constraints are considered in this dissertation,including the constraints of actuators and sensors in each agent,the constraints of the communication network,and the motion safety constraints of the multi-agent systems.Finally,to make the individual agent's model more relevant to the actual physical system,each agent's dynamics are modeled by the Euler-Lagrange equation which can be used to represent many practical mechanical systems because it is derived according to the conservation of energy.Based on these facts,this dissertation studies the formation-containment control problem of multi-agent systems with Euler-Lagrange dynamics by considering three types of constraints:constraints in each agent,communication constraints,and motion safety constraints.For each part of the research,this dissertation will design a formation control algorithm for the leaders,and design containment control algorithm for the followers.The main research contents and research results of this dissertation are as follows.First,for multi-agent formation-containment system with constraints on each agent,two types of constraints are primarily considered:the actuators are saturated and the rela-tive velocity information is unavailable for all agents.For the case that the actuator of each agent is saturated,the expected output of each system is estimated by designing an auxil-iary dynamic system,so that the system can finally asymptotically converge to the desired state.The gains of the saturated controller need to satisfy the condition that the sum of them is not greater than the saturation upper bound.For the case of no available relative velocity information on each agent,since the entire formation system is finally stationary after reaching the desired configuration,by replacing the relative velocity term directly with zero vector,the formation-containment system is proved to be stable by properly designing Lyapunov functions.However,the gain of the controller designed in this case needs to meet a graphic condition,which is related to the communication topology.To avoid this condition,the adaptive gain technique is used in the control algorithm design.For the multi-agent formation-containment system with communication constraints,two kinds of constraints are mainly considered:the communication delays and the dis-continuous communication between the agents.For the case with communication delays,unlike the case considered in the previous chapter,the speed of the formation-containment system here converges to a nonzero value.Therefore,the communication delays consid-ered in this case is consistent,that is,each communication delay between the agents is the same.To deal with the communication delay problem,we use the matrix inequality to de-scribe the stability condition and solve it through the Schur complement theorem.Finally,the variable gain technique is used to remove the parameter constraints.For the case that the communication cannot be continuously conducted,the event-triggered method is used to achieve the formation-containment control of the multi-agent systems.The advantages of event-triggered control include that the sampled communication is only performed at the time when the event function is triggered,so the communication frequency can be greatly reduced and the communication burden can be reduced.For multi-agent formation-containment control with motion safety constraints,two types of safety constraints are considered:collision avoidance between agents and obsta-cle avoidance between agents and environmental obstacles.For the collision avoidance problem between agents,the potential function-based approach is used,in which the gradi-ent of the potential function is added to the control algorithm.In the multi-agent collision avoidance system,each agent must be equipped with a distance sensor for distance detec-tion with all other agents in order to complete the collision avoidance.For the traditional obstacle avoidance problem,the potential function-based approaches are mostly used,and each agent is required to detect the exact position of the obstacle.This is hard to be satis-fied for the large-scale formation-containment systems.In this dissertation,we consider that the leaders will be equipped with obstacle detection sensors and responsible for tra-jectory planning,so that the leaders can complete the tracking of the planned trajectory to avoid the obstacle collision.The followers only need to follow the leaders because the follower is always in the leaders' convex hull.When the leaders do not collide with the obstacle,the follower will also not.The research of this dissertation can not only provide new methods for the future theoretical development of multi-agent systems,but also can be extended to practical en-gineering applications,for instance,multi-robot cooperative exploration,unmanned aerial vehicle formation flying,spacecraft formation flying control.