Optimal iterative learning control design for multi-agent systems consensus tracking

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• 作者：Shiping Yang^a ; ^b ; ^{yangshiping@nus.edu.sg" class="auth_mail} ; Jian-Xin Xu^b ; ^{elexujx@nus.edu.sg" class="auth_mail} ; Deqing Huang^c ; ^{elehd2012@gmail.com" class="auth_mail} ; Ying Tan^d ; ^{yingt@unimelb.edu.au" class="auth_mail}
• 关键词：Iterative learning control ; Consensus tracking ; Multi-agent systems ; Optimal design
• 刊名：Systems and Control Letters
• 出版年：July 2014
• 年：2014
• 卷：69
• 期：Complete
• 页码：80-89
• 全文大小：609 K

文摘

Under a repeatable operation environment, this paper proposes an iterative learning control scheme that can be applied to multi-agent systems to perform consensus tracking under the fixed communication topology. The agent dynamics are modeled by time-varying nonlinear equations which satisfy the global Lipschitz continuous condition. In addition, the desired consensus trajectory is only accessible to a subset of the followers. By using the concept of the graph dependent matrix norm, the convergence conditions can be specified at the agent level, which depend on a set of eigenvalues that are associated with the communication topology. The results are first derived for homogeneous agent systems and then extended to heterogeneous systems. Next, optimal controller gain design methods are proposed in the sense that the mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0167691114001005&_mathId=si2.gif&_user=111111111&_pii=S0167691114001005&_rdoc=1&_issn=01676911&md5=c92cdf35d5ceb5daedf912a5af0ffbc9" title="Click to view the MathML source">位mathContainer hidden">mathCode"><math altimg="si2.gif" overflow="scroll">位math>-norm of tracking error converges at the fastest rate, which imposes a tightest bounding function for the actual tracking error in the mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0167691114001005&_mathId=si3.gif&_user=111111111&_pii=S0167691114001005&_rdoc=1&_issn=01676911&md5=dfa2816e4f8a42f6dcab3254bb8897b7" title="Click to view the MathML source">位mathContainer hidden">mathCode"><math altimg="si3.gif" overflow="scroll">位math>-norm analysis framework. In the end, an illustrative example of a group of heterogeneous agents is provided to demonstrate the effectiveness of the proposed design methods.