时滞环境下具有不确定参数群系统的鲁棒一致性
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摘要
研究了普通线性群系统在存在时延和不确定参数条件下的鲁棒一致性问题。首先结合分布式PID控制和静态输出反馈提出一种新的一致性协议;然后引入描述符方法将闭环系统的微分方程转化为描述符模型,通过变量转换将一致性问题转化为渐近稳定问题;构造Lyapunov-Krasovskii泛函,基于线性矩阵不等式(LMI)给出了鲁棒控制器的设计方法。仿真结果表明:系统的结构拓扑图在存在全局可达节点的条件下,通过选择合适的PID参数,系统可实现一致性,且不确定参数会对系统的运动轨迹产生影响,通过与基于PD控制的一致性协议对比结果可知本文提出的一致性协议使得群系统收敛速度更快,鲁棒性更强。
Firstly, this paper proposes a novel protocol based on distributed PID control law and introduces a descriptor method to transform the differential equations of the closed systems into a descriptor model, transforming the consensus problem into an asymptotic stability problem. And then a Lyapunov-Krasovskii functional is constructed and the parameters of the consensus protocol are given based on the linear matrix inequality(LMI). The simulations show that if the topology contains a globally reachable node, through selecting appropriate PID parameters, the MAS can achieve consensus, and the uncertain parameters will cause bad effect to the trajectories of the systems. Compared with the PD-Control-Based consensus protocol, the proposed protocol makes the swarm systems converge faster, and the robustness stronger.
Firstly, this paper proposes a novel protocol based on distributed PID control law and introduces a descriptor method to transform the differential equations of the closed systems into a descriptor model, transforming the consensus problem into an asymptotic stability problem. And then a Lyapunov-Krasovskii functional is constructed and the parameters of the consensus protocol are given based on the linear matrix inequality(LMI). The simulations show that if the topology contains a globally reachable node, through selecting appropriate PID parameters, the MAS can achieve consensus, and the uncertain parameters will cause bad effect to the trajectories of the systems. Compared with the PD-Control-Based consensus protocol, the proposed protocol makes the swarm systems converge faster, and the robustness stronger.
引文
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[14] SUN Y G,WANG L,XIE G M.Average Consensus in Networks of Dynamic Agents with Switching Topologies and Multiple Time-Varying Delays[J].Systems & Control Letters,2008,57(2):175-183.
[15] HALE J,VERDUYN LUNEL S M.Introduction to Functional Differential Equations[M].New York,NY,USA:Springer-Verlag,1993.
[2] LYNCH N A.Distributed Algorithms[M].San Francisco:Morgan Kaufmann,1996.
[3] REN W,BEARD R W.Distributed Consensus in Multi-vehicle Cooperative Control:Theory and Applications[M].London:Springer-Verlag,2007.
[4] LAWTON J R,BEARD R W,YOUNG B.A Decentralized Approach to Formation Maneuvers[J].IEEE Transactions on Robotics and Automation,2003,19(6):933-941.
[5] YAN M D,ZHU X,ZHANG X X,et al.Consensus-Based Three-Dimensional Multi-UAV Formation Control Strategy with High Precision[J].Frontiers of Information Technology & Electronic Engineering,2017,18(7):968-977.
[6] TANNER H G.Flocking with Obstacle Avoidance in Switching Networks of Interconnected Vehicles[C]//IEEE Conference on Robotics and Automation,New Orleans,LA,USA,2004:3006-3011.
[7] 周艳杰,曹显兵,莫立坡.不确定二阶群系统的鲁棒最优一致[J].数学的实践与认识,2012,42(21):183-189.ZHOU Y J,CAO X B,MO L P.The Robust Optimal Consensus of Uncertain Second-Order Multi-Agent Systems[J].Mathematics in Practice and Theory,2012,42(21):183-189.(in Chinese)
[8] SHARIATI A,TAVAKOLI T.A Descriptor Approach to Robust Leader-Following Output Consensus of Uncertain Multi-Agent Systems with Delay[J].IEEE Transactions on Automatic Control,2016(99):1-8.
[9] SUN Y Z,LI W,RUAN J.Average Consensus of Multi-Agent Systems with Communication Time Delays and Noisy Links[J].Chinese Physics B,2013,22(3):262-270.
[10] CHEN Y,DONG H R,Lü J.Robust Consensus of Nonlinear Multiagent Systems with Switching Topology and Bounded Noises[J].IEEE Transactions on Cybernetics,2016,46(6):1276-1285.
[11] 曾耀武,冯伟.具有时滞和不确定性群鲁棒一致性研究[J].复杂系统与复杂性科学,2013,10(3):75-80.CENG Y W,FENG W.Robust Consensus Analysis of Multi-Agent Systems with Both Time-Delay and Uncertainty[J].Complex Systems and Complexity Science,2013,10(3):75-80.(in Chinese)
[12] MOON Y S,PARK P,KWON W H,et al.Delay-Dependent Robust Stabilization of Uncertain State-Delayed Systems[J].International Journal of Control,2004,74(14):1447-1455.
[13] WANG Y,XIE L,DE SOUZA CE.Robust Control of a Class of Uncertain Nonlinear Systems[J].Systems and Control Letters,1992,19(2):139-149.
[14] SUN Y G,WANG L,XIE G M.Average Consensus in Networks of Dynamic Agents with Switching Topologies and Multiple Time-Varying Delays[J].Systems & Control Letters,2008,57(2):175-183.
[15] HALE J,VERDUYN LUNEL S M.Introduction to Functional Differential Equations[M].New York,NY,USA:Springer-Verlag,1993.