Xi Jianxiang, Wang Xicong, Li Hongyao, Zhang Qi, Han Xinzhong
High-Tech Institute of Xi'an, Xi'an, 710025, China.
High-Tech Institute of Xi'an, Xi'an, 710025, China.
ISA Trans. 2022 Jan;120:235-246. doi: 10.1016/j.isatra.2021.03.029. Epub 2021 Mar 23.
This paper studies the energy-constraint output formation control for swarm systems with leaderless and leader-following topology structures. Most existing results on output formation with the dynamic output feedback protocols focus on the swarm systems without the energy constraint, but it is well known that the energy constraint is critically important for practical applications. In order to analyze the impacts of the energy constraint, a new energy-constraint output formation protocol is proposed. First, by the observable decomposition approach, a dynamic output formation protocol is presented, which contains an energy-constraint term to restrict the whole consumption. Then, sufficient conditions for leaderless energy-constraint output formation are presented via establishing the relationship of the energy constraint and the matrix variables, where it is found that the designed gain matrices of the output formation protocol can ensure that the actual energy consumption is lower than the total energy supply. Especially, a partition checking algorithm is proposed to check those conditions, which can ensure the scalability and solvability of a swarm system. Moreover, the output formation center function is derived to depict the whole macroscopic movement of a swarm system. A nonsingular transformation approach is presented to unify leaderless energy-constraint output formation and energy-constraint output formation tracking into the same framework, which are usually discussed in different theoretical frameworks. Finally, two simulation examples are illustrated to show that the theoretical results about leaderless energy-constraint output formation and energy-constraint output formation tracking are correct.
本文研究了具有无领导和有领导跟随拓扑结构的群体系统的能量约束输出编队控制问题。大多数关于动态输出反馈协议的现有输出编队结果都集中在没有能量约束的群体系统上，但众所周知，能量约束在实际应用中至关重要。为了分析能量约束的影响，提出了一种新的能量约束输出编队协议。首先，通过可观分解方法，给出了一种动态输出编队协议，该协议包含一个能量约束项以限制整体消耗。然后，通过建立能量约束与矩阵变量之间的关系，给出了无领导能量约束输出编队的充分条件，发现输出编队协议设计的增益矩阵可以确保实际能量消耗低于总能量供应。特别地，提出了一种分区检查算法来检查这些条件，这可以确保群体系统的可扩展性和可解性。此外，推导了输出编队中心函数来描述群体系统的整体宏观运动。提出了一种非奇异变换方法，将无领导能量约束输出编队和能量约束输出编队跟踪统一到同一个框架中，这两个问题通常在不同的理论框架下讨论。最后，给出了两个仿真例子，以表明关于无领导能量约束输出编队和能量约束输出编队跟踪的理论结果是正确的。
