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Distributed optimal consensus of multiple double integrators under bounded velocity and acceleration 
ZhirongQIU,LihuaXIE,YiguangHONG 

(School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798) 

摘要: 
This paper studies a distributed optimal consensus problem for multiple double integrators under bounded velocity and acceleration. Assigned with an individual and private convex cost which is dependent on the position, each agent needs to achieve consensus at the optimum of the aggregate cost under bounded velocity and acceleration. Based on relative positions and velocities to neighbor agents, we design a distributed control law by including the integration feedback of position and velocity errors. By employing quadratic Lyapunov functions, we solve the optimal consensus problem of doubleintegrators when the fixed topology is strongly connected and weightbalanced. Furthermore, if an initial estimate of the optimum can be known, then control gains can be properly selected to achieve an exponentially fast convergence under bounded velocity and acceleration. The result still holds when the relative velocity is not available, and we also discuss an extension for heterogeneous EulerLagrange systems by inverse dynamics control. A numeric example is provided to illustrate the result. 
关键词: Distributed optimization, double integrators, bounded velocity, bounded input 
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Distributed optimal consensus of multiple double integrators under bounded velocity and acceleration 
Zhirong QIU,Lihua XIE,Yiguang HONG 
(School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798;Key Laboratory of Systems and Control, Institute of Systems Science, Chinese Academy of Sciences, Beijing 100190, China) 
Abstract: 
This paper studies a distributed optimal consensus problem for multiple double integrators under bounded velocity and acceleration. Assigned with an individual and private convex cost which is dependent on the position, each agent needs to achieve consensus at the optimum of the aggregate cost under bounded velocity and acceleration. Based on relative positions and velocities to neighbor agents, we design a distributed control law by including the integration feedback of position and velocity errors. By employing quadratic Lyapunov functions, we solve the optimal consensus problem of doubleintegrators when the fixed topology is strongly connected and weightbalanced. Furthermore, if an initial estimate of the optimum can be known, then control gains can be properly selected to achieve an exponentially fast convergence under bounded velocity and acceleration. The result still holds when the relative velocity is not available, and we also discuss an extension for heterogeneous EulerLagrange systems by inverse dynamics control. A numeric example is provided to illustrate the result. 
Key words: Distributed optimization, double integrators, bounded velocity, bounded input 




