合作竞争共存机制下网络化Lagrange系统复合任务协调的分析与控制

The main objective of this project is to investigate the multi-task coordinated control problems for networked Lagrangian systems under the coexistence of cooperation and competition among the systems. Built upon our recent work on the coordinated control of networked Lagrangian systems, this project is mainly focused on the following two issues: Firstly, under group structure network topology, the dynamic group consensus control for the systems without input disturbances and the group regional consensus for the systems with input disturbances will be studied, then the corresponding group consensus protocols and the evolution mechanisms of group consensus will be established. Secondly, under structurally balanced network topology, the bipartite consensus problem for the systems without input disturbances and the practical bipartite consensus for the systems with input disturbances will be investigated, and some bipartite consensus control algorithms together with the corresponding stability criteria will be constructed. It is believed that the research results of this project will not only develop a deep understanding of the cooperation and evolution mechanisms and the coordinated control principle of networked Lagrangian systems in competitive network environments, but also provide some new insights into and novel methods for the design of intelligent robot systems modeled by networked Lagrangian systems.

本项目主要研究合作竞争共存网络机制下Lagrange系统的复合任务协调控制问题。基于申请人近年来在网络化Lagrange系统协调控制方面已有的工作基础，主要关注以下两方面内容：在具有分群结构的网络环境下，研究网络化Lagrange系统动态分群一致以及带扰动输入的网络化系统区域分群一致协调控制问题，给出相应的分群一致控制协议并探索系统分群一致的演化机制；在具有平衡结构的网络环境下，研究网络化Lagrange系统双边一致以及带扰动输入的实用双边一致协调控制问题，建立系统双边一致控制策略和相应的稳定性判据。本项目的研究有助于揭示合作竞争共存环境下网络化Lagrange系统合作演化的机制和协调控制原理，为网络化Lagrange系统所能刻画的智能机器人等系统的设计提供新的方法和思想。

本项目通过拓展网络系统的双边一致和分群一致的概念来刻画多机器人系统的复合任务控制目标，并针对Lagrange系统描述的网络化集群机器人系统提出了合理的分布式复合任务控制算法，主要结论如下：1. 通过结合分群一致和双边一致的特点，提出了分群—双边一致的概念，并在无循环划分以及平衡耦合两种拓扑结构下给出了一种分布式分群—双边一致的控制算法。2. 研究了Lagrange系统刻画的系数不确定集群机器人系统双边一致问题，给出了相应的控制算法。利用拉普拉斯矩阵特殊的结构，我们构造了一种新型的分解矩阵来进行受控闭环系统的收敛性分析。3. 研究了Lagrange方程描述的集群机器人系统双边一致问题，给出了相应的控制算法。相比较内容2，这里给出了系统最终收敛状态的显式表达式。同时，我们设计的控制器可以能在简单的代数条件下就能实现网络化Lagrange系统复合任务，因而具有重要的实际应用价值。