Sliding Mode Formation Optimization for Multi-Agent Systems With Unknown Disturbances in Predefined Time
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摘要: 针对无领导者的多智能体系统，研究未知干扰下实现任意预设时间分布式编队优化的问题，最小化所有智能体局部强凸函数构成的全局代价函数. 提出一类基于滑模控制的编队优化算法，能够在用户预设的时间内实现多智能体系统的编队控制. 该算法分为三个部分：首先，采用积分滑模控制策略，引导预设时间内每个智能体趋于滑模面，有效地抑制外部干扰；然后，设计协议控制引导每个智能体状态到达其局部代价函数的最小值点；最后，所有智能体实现无领导编队，且到达全局代价函数的最小值点. 该算法无需智能体共享邻居的梯度和Hesse矩阵信息，从而节约信息交换成本，可以处理高度非线性多值强凸代价函数. 数值实验的多个例子验证了设计控制协议算法的有效性和可靠性.Abstract: For leader-less multi-agent systems, the problem of distributed formation optimization in predefined time under unknown disturbances was studied, and the global cost function composed of local strongly convex functions for all agents was minimized. A class of formation optimization algorithms based on the sliding mode control was proposed to realize the formation control of multi-agent systems within the predefined time. The algorithm was divided into 3 parts: firstly, the integrated sliding mode control strategy was used to guide each agent to approach the sliding mode surface in the predefined time, and the external interference was effectively suppressed; then, the design protocol control was employed to guide each agent state to the minimum point of its local cost function; finally, the leaderless formation was realized for all agents to reach the minimum point of the global cost function. The algorithm does not require agents to share the gradients and Hessian matrix information of neighbors, thus saving the information exchange cost, and can deal with highly nonlinear multi-valued strongly convex cost functions. Several examples of numerical experiments demonstrate the effectiveness and reliability of the design control protocol algorithm.
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图 2 预设时间收敛的状态xi(t), i=1, 2, …, 6演化图
注 为了解释图中的颜色, 读者可以参考本文的电子网页版本, 后同.
Figure 2. State evolution xi, i=1, 2, …, 6 of the predefined-time convergence
图 3 有限时间收敛的状态xi(t), i=1, 2, …, 6演化图
Figure 3. State evolution xi, i=1, 2, …, 6 of the finite-time convergence
图 4 固定时间收敛的状态xi(t), i=1, 2, …, 6演化图
Figure 4. State evolution xi, i=1, 2, …, 6 of the fixed-time convergence
图 7 未知干扰下全局代价函数F( p(t))演化图
Figure 7. The evolution of F(p(t)) under unknown disturbances
表 1 时间数据对比分析
Table 1. Comparative analysis of time data
time to reach the local minimum/s time to reach the global minimum/s finite time no 4.032 8 fixed time 0.686 8 3.470 2 predefined time 1 1.5 
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