复杂环境下多智能体系统一致性研究
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摘要
实践中多智能体系统所处的环境是复杂的,不可避免会受到多种约束因素的影响,比如:有限的通信带宽、不同特性的测量噪声、不同因素引起的时延、不稳定的连接结构等.具体到研究多智能体系统的协调控制时,包括一致性、同步控制、跟随控制、编队控制等,根据智能体所处的特定网络化环境,有针对性的考虑特定的一个或者几个约束因素的影响具有重要的理论研究意义和实践应用价值.本论文在前人研究的基础上进一步考虑了复杂环境下多智能体系统的一致性问题.针对特定环境下的多智能体系统,既研究了经典的一致性控制协议对各类约束因素的敏感性和鲁棒性,也设计了新的一致性协议来实现相应环境下多智能体系统的一致性.同时也考虑了用相应的一致性协议来研究复杂环境下线性和非线性多智能体系统的同步控制和跟随控制.
本论文的主要工作有以下几个方面:
1.概述了多智能体系统的协调控制,特别是一致性的相关背景、研究意义和研究现状,并阐明了本论文研究工作的价值和意义、难点和创新之处.
2.进一步研究了数字网络环境下多智能体系统的一致性问题.针对具有带宽约束的多智能体系统,证明了现有文献中的平均一致性协议对不同类型的时延具有不同的敏感性.表明了该平均一致性控制协议对于有限对称时延具有良好的鲁棒性,但对于非对称时延却是敏感的,非对称时延一般会破坏该环境下的平均一致性.同时也设计了新的一致性协议去研究该平均一致性问题.在考虑对称网络拓扑结构情形的基础上,也研究了非对称网络拓扑结构环境下具有带宽约束的多智能体系统的加权平均一致性,所设计的协议可以在该环境下实现多智能体系统的加权平均一致性.
3.利用广义Nyquist稳定性准则和Gersgorin圆盘定理,本论文进一步研究了具有多种时延约束的连续时间多智能体系统的加权平均一致性.表明了经典的一致性控制协议对于个体间的通信时延以及个体自身的时延都具有良好的鲁棒性;也表明了不同的时延对多智能体系统一致性的影响是有区别的.一般地个体间的有限通信时延不会破坏多智能体系统实现一致性,但会改变智能体之间的共识值;对于给定的多智能体系统,太大的自时延会破坏多智能体系统的一致性.
4.研究了具有测量噪声约束的线性和非线性多智能体系统的同步控制,分别考虑了加性和乘性两类测量噪声的约束.针对不同性质的测量噪声,分别设计了不同的一致性协议去实现线性和非线性多智能体系统的同步控制.表明了在均方意义下传统的一致性控制协议对乘性测量噪声具有良好的鲁棒性,但对加性测量噪声却不具有良好的鲁棒性.进一步,在考虑测量噪声约束的同时也考虑了外源扰动约束因素,研究了非线性多智能体系统的保性能平均同步控制和保性能跟随控制.
5.进一步研究了具有测量噪声约束的领导者跟随者系统的跟随控制.分别在固定和切换拓扑网络结构下,研究了具有测量噪声约束的领导者跟随者系统的跟随控制,表明了在均方意义下传统的跟随控制协议对依赖于测量值的测量噪声具有良好的鲁棒性.
最后对本论文进行了总结归纳.
The practical environments for multi-agent systems are complex. There exist a lotof constraints, such as limited communication bandwidth, measurement noises with dif-ferent characteristics, time-delays caused by diferent factors, unstable connection struc-ture, and so on. It has important theoretical and practical signifcance to consider theseconstraints, when we study the coordination control of multi-agent systems, includingconsensus, synchronization control, tracking control, formation control, etc. Based onthe previous studies, this dissertation will further research the coordination control ofmulti-agent systems under complex environments, in particularly the consensus. Undercomplex environmental conditions, we further study the traditional consensus protocolsof multi-agent systems. And we also design some new consensus protocols for certaincircumstances. At the same time, we also study the synchronization and tracking controlwith constraints.
The main contributions of this dissertation are summarized as follows.
1. The background, research signifcance and current situation of the selected topicare reviewed. Then, we indicate the signifcance, difculties and innovations of the dis-sertation.
2. Under the digital network environment, the consensus of multi-agent systemsis studied. First, we study the average consensus of multi-agent systems with limitedbandwidth and time-delays. It is proved that the average consensus protocols existed inliteratures have diferent sensitivity for diferent delays. The average consensus protocolexisted in literatures is robust to the fnite symmetric delays. But it is sensitive to theasymmetric delays. Generally, the asymmetric delays would destroy the average consensusof multi-agent systems with limited bandwidth. Furthermore, we also designed some newprotocols to study the average consensus under the same network environment. For theasymmetric network environment, we further studied the weighted average consensus.
3. Using the generalized Nyquist stability criterion and Gersgorin disc theorem, theweighted average consensus of continuous-time multi-agent systems with diverse time-delays is considered. It is shown that the classical consensus protocol is robust to time-delays (include communication time-delays among agents and self time-delays of eachagent). It is also shown that the classical consensus protocol has diferent properties fordiferent time-delays. Generally, the consensus of continuous-time multi-agent systemscan not be destroyed by fnite communication time-delays. But the value of consensus would be changed. For a given continuous-time multi-agent systems, the consensus wouldbe destroyed by the too big self time-delays of agents.
4. The synchronization of linear and nonlinear multi-agent systems with measure-ment noises is studied. The additive and multiplicative measurement noises are consid-ered respectively, when we study the synchronization of multi-agent systems. In order toachieve synchronization, we design diferent protocols for diferent measurement noises.It is shown that the traditional synchronization control protocol is robust to the multi-plicative measurement noises in mean square. But it has not good robustness to additivemeasurement noises. Furthermore, the synchronization with a guaranteed H∞perfor-mance is studied. It is shown that all agents can achieve synchronization in mean squareand meanwhile maintain a desirable disturbance rejection performance. We also considerthe tracking problem with a guaranteed H∞performance for a leader-follower nonlinearmulti-agent system.
5. Under the fxed and switched topology structure, the tracking control of multi-agent systems with an active leader and measurement noises is studied. It is shown thatthe traditional control protocol has good robustness to the measurement noises whichdepend on the measurement value.
Finally, the main results of the dissertation are concluded.
本论文的主要工作有以下几个方面:
1.概述了多智能体系统的协调控制,特别是一致性的相关背景、研究意义和研究现状,并阐明了本论文研究工作的价值和意义、难点和创新之处.
2.进一步研究了数字网络环境下多智能体系统的一致性问题.针对具有带宽约束的多智能体系统,证明了现有文献中的平均一致性协议对不同类型的时延具有不同的敏感性.表明了该平均一致性控制协议对于有限对称时延具有良好的鲁棒性,但对于非对称时延却是敏感的,非对称时延一般会破坏该环境下的平均一致性.同时也设计了新的一致性协议去研究该平均一致性问题.在考虑对称网络拓扑结构情形的基础上,也研究了非对称网络拓扑结构环境下具有带宽约束的多智能体系统的加权平均一致性,所设计的协议可以在该环境下实现多智能体系统的加权平均一致性.
3.利用广义Nyquist稳定性准则和Gersgorin圆盘定理,本论文进一步研究了具有多种时延约束的连续时间多智能体系统的加权平均一致性.表明了经典的一致性控制协议对于个体间的通信时延以及个体自身的时延都具有良好的鲁棒性;也表明了不同的时延对多智能体系统一致性的影响是有区别的.一般地个体间的有限通信时延不会破坏多智能体系统实现一致性,但会改变智能体之间的共识值;对于给定的多智能体系统,太大的自时延会破坏多智能体系统的一致性.
4.研究了具有测量噪声约束的线性和非线性多智能体系统的同步控制,分别考虑了加性和乘性两类测量噪声的约束.针对不同性质的测量噪声,分别设计了不同的一致性协议去实现线性和非线性多智能体系统的同步控制.表明了在均方意义下传统的一致性控制协议对乘性测量噪声具有良好的鲁棒性,但对加性测量噪声却不具有良好的鲁棒性.进一步,在考虑测量噪声约束的同时也考虑了外源扰动约束因素,研究了非线性多智能体系统的保性能平均同步控制和保性能跟随控制.
5.进一步研究了具有测量噪声约束的领导者跟随者系统的跟随控制.分别在固定和切换拓扑网络结构下,研究了具有测量噪声约束的领导者跟随者系统的跟随控制,表明了在均方意义下传统的跟随控制协议对依赖于测量值的测量噪声具有良好的鲁棒性.
最后对本论文进行了总结归纳.
The practical environments for multi-agent systems are complex. There exist a lotof constraints, such as limited communication bandwidth, measurement noises with dif-ferent characteristics, time-delays caused by diferent factors, unstable connection struc-ture, and so on. It has important theoretical and practical signifcance to consider theseconstraints, when we study the coordination control of multi-agent systems, includingconsensus, synchronization control, tracking control, formation control, etc. Based onthe previous studies, this dissertation will further research the coordination control ofmulti-agent systems under complex environments, in particularly the consensus. Undercomplex environmental conditions, we further study the traditional consensus protocolsof multi-agent systems. And we also design some new consensus protocols for certaincircumstances. At the same time, we also study the synchronization and tracking controlwith constraints.
The main contributions of this dissertation are summarized as follows.
1. The background, research signifcance and current situation of the selected topicare reviewed. Then, we indicate the signifcance, difculties and innovations of the dis-sertation.
2. Under the digital network environment, the consensus of multi-agent systemsis studied. First, we study the average consensus of multi-agent systems with limitedbandwidth and time-delays. It is proved that the average consensus protocols existed inliteratures have diferent sensitivity for diferent delays. The average consensus protocolexisted in literatures is robust to the fnite symmetric delays. But it is sensitive to theasymmetric delays. Generally, the asymmetric delays would destroy the average consensusof multi-agent systems with limited bandwidth. Furthermore, we also designed some newprotocols to study the average consensus under the same network environment. For theasymmetric network environment, we further studied the weighted average consensus.
3. Using the generalized Nyquist stability criterion and Gersgorin disc theorem, theweighted average consensus of continuous-time multi-agent systems with diverse time-delays is considered. It is shown that the classical consensus protocol is robust to time-delays (include communication time-delays among agents and self time-delays of eachagent). It is also shown that the classical consensus protocol has diferent properties fordiferent time-delays. Generally, the consensus of continuous-time multi-agent systemscan not be destroyed by fnite communication time-delays. But the value of consensus would be changed. For a given continuous-time multi-agent systems, the consensus wouldbe destroyed by the too big self time-delays of agents.
4. The synchronization of linear and nonlinear multi-agent systems with measure-ment noises is studied. The additive and multiplicative measurement noises are consid-ered respectively, when we study the synchronization of multi-agent systems. In order toachieve synchronization, we design diferent protocols for diferent measurement noises.It is shown that the traditional synchronization control protocol is robust to the multi-plicative measurement noises in mean square. But it has not good robustness to additivemeasurement noises. Furthermore, the synchronization with a guaranteed H∞perfor-mance is studied. It is shown that all agents can achieve synchronization in mean squareand meanwhile maintain a desirable disturbance rejection performance. We also considerthe tracking problem with a guaranteed H∞performance for a leader-follower nonlinearmulti-agent system.
5. Under the fxed and switched topology structure, the tracking control of multi-agent systems with an active leader and measurement noises is studied. It is shown thatthe traditional control protocol has good robustness to the measurement noises whichdepend on the measurement value.
Finally, the main results of the dissertation are concluded.
引文
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