分布式多智能体系统一致性问题研究
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摘要
近年来,随着分布式多智能体系统的迅速发展,分布式协作控制成为控制领域研究的一个热点。多智能体协作控制研究的是大量只具简单功能的个体如何通过分布式的控制,相互合作,产生复杂的群体行为。一致性问题作为多智能体之间合作协调的基础,受到来自各个领域研究者越来越多的关注。在多智能体系统中,“一致性”是指智能体就某些状态量趋于相同,而一致性算法是指多个智能体基于局部信息采取的使得个体状态趋于一致的协议。本论文重点分析了具有状态预测器的一致性算法;把状态预测器的策略应用到多智能体编队和覆盖问题;分析了通讯延迟对具有状态预测器的多智能体系统收敛性的影响;研究了在有输入饱和约束情况下一致性算法的收敛条件。
本论文的主要内容和研究成果总结如下:
1.具有状态预测器的多智能体系统一致性研究。提出了一种状态预测器,以一次通讯的代价提高了多智能体系统的最小非零特征值,进而提高了多智能体系统达到一致的速度;把状态预测器应用于二阶多智能体系统的一致性算法,通过仿真验证了状态预测器的引入提高了系统完成任务的速度。
2.具有状态预测器的编队和覆盖问题性能分析。在分布式多智能体系统编队算法中引入状态预测器,以提高分布式多智能体系统完成编队任务的速度;在分布式多智能体系统覆盖算法中应用状态预测器,以提高多智能体系统完成覆盖任务的速度。并通过仿真验证了状态预测器引入的有效性。
3.通讯延迟对于多智能体系统一致性演化的影响。由于通讯存在延迟,当通讯延迟过大时,无延迟时能渐近一致的多智能系统将不再能渐近的一致,论文分析了状态预测器的引入对系统允许延迟裕量的影响,指出由于多次通讯,算法对时延的鲁棒性比无状态预测时有所削弱。
4.有饱和约束的多智能体系统一致性算法分析。对有饱和约束的多智能体系统,在控制律保持不变的情况下进行了分析,给出了分布式多智能体系统中控制量存在饱和约束时多智能体系统仍能渐近一致的条件。
In recent years, with the rapid development of distributed multi-agent systems, distributed cooperative control research becomes a hot spot in the field of control science research. The cooperative control of multi-agents investigates how a large number of individuals with simple function can perform complicated tasks or achieve cooperative group behaviors by distributed control. As the basis of the cooperative control of multi-agents, consensus problem attracts much attention from many different fields. In a multi-agent system, consensus means that some of the agents’states reach at the same values, and consensus algorithm is a protocol for agents reach consensus based on local information. This thesis focuses on the consensus algorithm with state predictor; the state predictor strategy applied to the multi-agent formation and coverage problems; the impact of communication delay on group convergence; the sufficient condition of convergence of consensus algorithm with input saturation.
The main contributions of this dissertation are summarized as follows:
1. Study on a consensus algorithm with a state predictor. In order to improve the performance of a consensus algorithm, this thesis presents a state predictor strategy, and under this strategy, the smallest non-zero eigenvalue of Laplacian Matrix can be increased. As a result, the performance is improved greatly. The state predictor strategy can also be applied to the second-order multi-agent system consensus algorithm. Simulations are introduced to show that state predictor is effective to raise the speed of the system to complete the task.
2. The performance analysis of formation and coverage algorithm with state predictor strategy. A distributed multi-agent system’s formation algorithm with the state predictor algorithm is introduced to improve the performance of the distributed multi-agent system to complete the formation task; and a distributed multi-agent systems coverage algorithm with the state predictor strategy is also introduced to improve the performance of the distributed multi-agent system to complete the coverage task. Simulations are given to verify the effectiveness of the state predictor strategy.
3. Study on effects of communication delay to the evolution of multi-agent system. If the communication delay is too large, multi-agent systems maybe fail to achieve consensus, and the robustness with respect to communication delay of Multi-agent system with state predictor is weaker than that of Multi-agent system without state predictor. Furthermore, the maximum communication delay is studied.
4. Analysis of Multi-agent system consensus algorithm with input saturation. When consensus can be achieved without input constraints, a sufficient condition that the multi-agent system still achieving consensus with respect to input saturation is presented.
本论文的主要内容和研究成果总结如下:
1.具有状态预测器的多智能体系统一致性研究。提出了一种状态预测器,以一次通讯的代价提高了多智能体系统的最小非零特征值,进而提高了多智能体系统达到一致的速度;把状态预测器应用于二阶多智能体系统的一致性算法,通过仿真验证了状态预测器的引入提高了系统完成任务的速度。
2.具有状态预测器的编队和覆盖问题性能分析。在分布式多智能体系统编队算法中引入状态预测器,以提高分布式多智能体系统完成编队任务的速度;在分布式多智能体系统覆盖算法中应用状态预测器,以提高多智能体系统完成覆盖任务的速度。并通过仿真验证了状态预测器引入的有效性。
3.通讯延迟对于多智能体系统一致性演化的影响。由于通讯存在延迟,当通讯延迟过大时,无延迟时能渐近一致的多智能系统将不再能渐近的一致,论文分析了状态预测器的引入对系统允许延迟裕量的影响,指出由于多次通讯,算法对时延的鲁棒性比无状态预测时有所削弱。
4.有饱和约束的多智能体系统一致性算法分析。对有饱和约束的多智能体系统,在控制律保持不变的情况下进行了分析,给出了分布式多智能体系统中控制量存在饱和约束时多智能体系统仍能渐近一致的条件。
In recent years, with the rapid development of distributed multi-agent systems, distributed cooperative control research becomes a hot spot in the field of control science research. The cooperative control of multi-agents investigates how a large number of individuals with simple function can perform complicated tasks or achieve cooperative group behaviors by distributed control. As the basis of the cooperative control of multi-agents, consensus problem attracts much attention from many different fields. In a multi-agent system, consensus means that some of the agents’states reach at the same values, and consensus algorithm is a protocol for agents reach consensus based on local information. This thesis focuses on the consensus algorithm with state predictor; the state predictor strategy applied to the multi-agent formation and coverage problems; the impact of communication delay on group convergence; the sufficient condition of convergence of consensus algorithm with input saturation.
The main contributions of this dissertation are summarized as follows:
1. Study on a consensus algorithm with a state predictor. In order to improve the performance of a consensus algorithm, this thesis presents a state predictor strategy, and under this strategy, the smallest non-zero eigenvalue of Laplacian Matrix can be increased. As a result, the performance is improved greatly. The state predictor strategy can also be applied to the second-order multi-agent system consensus algorithm. Simulations are introduced to show that state predictor is effective to raise the speed of the system to complete the task.
2. The performance analysis of formation and coverage algorithm with state predictor strategy. A distributed multi-agent system’s formation algorithm with the state predictor algorithm is introduced to improve the performance of the distributed multi-agent system to complete the formation task; and a distributed multi-agent systems coverage algorithm with the state predictor strategy is also introduced to improve the performance of the distributed multi-agent system to complete the coverage task. Simulations are given to verify the effectiveness of the state predictor strategy.
3. Study on effects of communication delay to the evolution of multi-agent system. If the communication delay is too large, multi-agent systems maybe fail to achieve consensus, and the robustness with respect to communication delay of Multi-agent system with state predictor is weaker than that of Multi-agent system without state predictor. Furthermore, the maximum communication delay is studied.
4. Analysis of Multi-agent system consensus algorithm with input saturation. When consensus can be achieved without input constraints, a sufficient condition that the multi-agent system still achieving consensus with respect to input saturation is presented.
引文
[1] Olfati-Saber R. and Murray R. M.,Consensus problems in networks of agents with switching topology and time-delays, IEEE Trans. on Automatic Control, 2004,49(9): 1520-1533.
[2] Kim Yoonsoo and Mesbahi Mehran,On Maximizing the Second Smallest Eigenvalue of a State-dependent Graph Laplacian, IEEE Trans. on Automatic Control, 2006, 51(1):116-120
[3] Li Xiaoli, Xi Yugeng, Distributed Formation Algorithm for Multi-agent Systems with a Relaxed Connectivity Condition. The 17th IFAC World Congress, July 6-11, 2008, Seoul, Korea.
[4] Godsil C., Royle G., Algebraic Graph Theory, Graduate Texts in Mathematics, Vol. 207, Springer, Berlin, 2001.
[5] Horn R. A. and Johnson C. R., Matrix Analysis. Cambridge University Press, 1985.
[6] Ren W, Beard RW., Distributed Consensus in Multi-vehicle Cooperative Control,Springer,2007.
[7] Li Xiaoli, Xi Yugeng, Space Coverage Control for Distributed Multi-Agent Systems with Preserved Connectivity. The 7th Asian Control Conference .August,2009, Hong Kong, China.
[8] Hu, Lin Z., Control Systems with Actuator Saturation: Analysis and Design, BirkhVauser, Boston, 2001.
[9] Cao YY, Lin Z., Set invariance analysis and gain-scheduling control for LPV system subject to actuator saturation. System & Control letters 2002,46:137-151.
[10] Moreau L. Stability of multi-agent systems with time-dependent communication links. IEEE Trans. on Automatic Control,2005, 50(2):169–182.
[11] Olfati-Saber R., Flocking for multi-agent dynamic systems: algorithms andtheory. . IEEE Trans. on Automatic Control, 2006,51(3): 401–420.
[12] Lafferriere G., Williams A., Caughman J., Veerman J.J.P., Decentralized control of vehicle formations. Systems & Control Letters , 2005,54: 899– 910
[13] Olfati-Saber Reza, Flocking for Multi-Agent Dynamic Systems: Algorithms and Theory IEEE Trans. on Automatic Control, 2006,51(3) .
[14] Ando H., Oasa Y., Suzuki I., and Yamashita, Distributed memoryless point convergence algorithm for mobile robots with limited visibility,”IEEE Trans. on Robot. Automatic., 1999,15(5) : 818–828.
[15] Gazi V. and Passino K. M., Stability analysis of swarms, IEEE Trans. Automatic Control, 2003,48(4):692–697.
[16] Dimos V. Dimarogonas and Kostas J. Kyriakopoulos, On the Rendezvous Problem for Multiple Nonholonomic Agents, IEEE Trans. on Automatic Control,2007,52(5).
[17] Cortes J., Martinez S., and Bullo F., Robust rendezvous for mobile autonomous agents via proximity graphs in arbitrary dimensions, IEEE Trans. Automatic Control, 2006,51(8):1289–1298.
[18] Seapahn Megerian, Farinaz Koushanfar, Miodrag Potkonjak, Mani B. Srivastava, Worst and Best-Case Coverage in Sensor Networks, IEEE Trans. on Mobile Computing, 2005,4(1).
[19] Chen Fei, Chen Zengqiang, Liu Zhongxin, Xiang Linying, Yuan Zhuzhi, Decentralized formation control of mobile agents: A unified framework , Physica A,2007,387: 4917–4926
[20] Lin J., Morse A. S., Anderson S. D. O., The multi-agent rendezvous problem. In Proceedings of IEEE Conference on Decision and Control, 2003, pp.1508-1513.
[21] Khatib O., Real-time obstacle avoidance for manipulators and mobile robots. Int. Journal of Robotics Research, 1986,5(1):90–98.
[22] Ando Hideki, Oasa Yoshinobu, Suzuki Ichiro, Distributed Memoryless Point Convergence Algorithm for Mobile Robots with Limited Visibility. IEEE Transaction on Robotics
[23] Hindi H., Boyd S., Analysis of linear systems with saturation using convex Control, optimization[C]. Proceedings of the conference on Decision and 1998, (1):903-908
[24] Tarbouriech S., Peres P. L. D., Garcia G., Queinnec I.. Delay-dependent stabilization of time-delay systems with saturating actuators. IEE Proceedings on Control Theory and Applications, 2002, 149(5): 387-393.
[25] Tarbouriech S., Garcia G., Gomes J. M., Robust stability of uncertain polytopic linear time-delay systems with saturating inputs: an LMI approach[J]. Computer and Electrical Engineering, 2002, 28(3): 157-169.
[26] Hu T., Lin Z., Chen B. M., An analysis an design method for linear systems subject to actuator saturation and disturbance, Automatica, 2002, 38(2):351-359.
[27] Hu T., Lin Z., Chen B. M., Analysis and design for discrete-time systems subject to actuator saturation. Systems and Control Letters, 2002, 45(2):87-112.
[28] Olfati-Saber R, Fax J A ,Murray R M. Consensus and cooperation in networked multi-agent systems. Proceedings of the IEEE,2007,95(1):215-233
[29]魏爱荣.饱和控制系统稳定性及干扰抑制研究.山东大学博士论文. 2006.
[30]刘太珲.状态饱和系统分析.浙江大学硕士学位论文. 2007.
[31] Murray Richard M., Recent Research in Cooperative Control of Multi-Vehicle Systems, International Conference on Advances in Control and Optimization of Dynamical Systems, 2007.
[2] Kim Yoonsoo and Mesbahi Mehran,On Maximizing the Second Smallest Eigenvalue of a State-dependent Graph Laplacian, IEEE Trans. on Automatic Control, 2006, 51(1):116-120
[3] Li Xiaoli, Xi Yugeng, Distributed Formation Algorithm for Multi-agent Systems with a Relaxed Connectivity Condition. The 17th IFAC World Congress, July 6-11, 2008, Seoul, Korea.
[4] Godsil C., Royle G., Algebraic Graph Theory, Graduate Texts in Mathematics, Vol. 207, Springer, Berlin, 2001.
[5] Horn R. A. and Johnson C. R., Matrix Analysis. Cambridge University Press, 1985.
[6] Ren W, Beard RW., Distributed Consensus in Multi-vehicle Cooperative Control,Springer,2007.
[7] Li Xiaoli, Xi Yugeng, Space Coverage Control for Distributed Multi-Agent Systems with Preserved Connectivity. The 7th Asian Control Conference .August,2009, Hong Kong, China.
[8] Hu, Lin Z., Control Systems with Actuator Saturation: Analysis and Design, BirkhVauser, Boston, 2001.
[9] Cao YY, Lin Z., Set invariance analysis and gain-scheduling control for LPV system subject to actuator saturation. System & Control letters 2002,46:137-151.
[10] Moreau L. Stability of multi-agent systems with time-dependent communication links. IEEE Trans. on Automatic Control,2005, 50(2):169–182.
[11] Olfati-Saber R., Flocking for multi-agent dynamic systems: algorithms andtheory. . IEEE Trans. on Automatic Control, 2006,51(3): 401–420.
[12] Lafferriere G., Williams A., Caughman J., Veerman J.J.P., Decentralized control of vehicle formations. Systems & Control Letters , 2005,54: 899– 910
[13] Olfati-Saber Reza, Flocking for Multi-Agent Dynamic Systems: Algorithms and Theory IEEE Trans. on Automatic Control, 2006,51(3) .
[14] Ando H., Oasa Y., Suzuki I., and Yamashita, Distributed memoryless point convergence algorithm for mobile robots with limited visibility,”IEEE Trans. on Robot. Automatic., 1999,15(5) : 818–828.
[15] Gazi V. and Passino K. M., Stability analysis of swarms, IEEE Trans. Automatic Control, 2003,48(4):692–697.
[16] Dimos V. Dimarogonas and Kostas J. Kyriakopoulos, On the Rendezvous Problem for Multiple Nonholonomic Agents, IEEE Trans. on Automatic Control,2007,52(5).
[17] Cortes J., Martinez S., and Bullo F., Robust rendezvous for mobile autonomous agents via proximity graphs in arbitrary dimensions, IEEE Trans. Automatic Control, 2006,51(8):1289–1298.
[18] Seapahn Megerian, Farinaz Koushanfar, Miodrag Potkonjak, Mani B. Srivastava, Worst and Best-Case Coverage in Sensor Networks, IEEE Trans. on Mobile Computing, 2005,4(1).
[19] Chen Fei, Chen Zengqiang, Liu Zhongxin, Xiang Linying, Yuan Zhuzhi, Decentralized formation control of mobile agents: A unified framework , Physica A,2007,387: 4917–4926
[20] Lin J., Morse A. S., Anderson S. D. O., The multi-agent rendezvous problem. In Proceedings of IEEE Conference on Decision and Control, 2003, pp.1508-1513.
[21] Khatib O., Real-time obstacle avoidance for manipulators and mobile robots. Int. Journal of Robotics Research, 1986,5(1):90–98.
[22] Ando Hideki, Oasa Yoshinobu, Suzuki Ichiro, Distributed Memoryless Point Convergence Algorithm for Mobile Robots with Limited Visibility. IEEE Transaction on Robotics
[23] Hindi H., Boyd S., Analysis of linear systems with saturation using convex Control, optimization[C]. Proceedings of the conference on Decision and 1998, (1):903-908
[24] Tarbouriech S., Peres P. L. D., Garcia G., Queinnec I.. Delay-dependent stabilization of time-delay systems with saturating actuators. IEE Proceedings on Control Theory and Applications, 2002, 149(5): 387-393.
[25] Tarbouriech S., Garcia G., Gomes J. M., Robust stability of uncertain polytopic linear time-delay systems with saturating inputs: an LMI approach[J]. Computer and Electrical Engineering, 2002, 28(3): 157-169.
[26] Hu T., Lin Z., Chen B. M., An analysis an design method for linear systems subject to actuator saturation and disturbance, Automatica, 2002, 38(2):351-359.
[27] Hu T., Lin Z., Chen B. M., Analysis and design for discrete-time systems subject to actuator saturation. Systems and Control Letters, 2002, 45(2):87-112.
[28] Olfati-Saber R, Fax J A ,Murray R M. Consensus and cooperation in networked multi-agent systems. Proceedings of the IEEE,2007,95(1):215-233
[29]魏爱荣.饱和控制系统稳定性及干扰抑制研究.山东大学博士论文. 2006.
[30]刘太珲.状态饱和系统分析.浙江大学硕士学位论文. 2007.
[31] Murray Richard M., Recent Research in Cooperative Control of Multi-Vehicle Systems, International Conference on Advances in Control and Optimization of Dynamical Systems, 2007.