用最优控制方法实现多智能体群体形状精准调控
Formation Shape Control using the Gromov-Wasserstein Metric
- 基于格罗莫夫-沃瑟斯坦距离设计形状控制目标函数
- 采用半定规划松弛技术解决高难度优化问题
- 适用于需要精确编队的多智能体系统场景
本文提出一种基于最优控制框架的群组形状控制算法，通过引入格罗莫夫-沃瑟斯坦距离，将初始智能体群体引导至期望配置。系统假设为约束线性动力学系统，代价函数由二次阶段成本和格罗莫夫-沃瑟斯坦终端成本组成。由于该距离导致问题变为经典的NP难问题，求解复杂且精度难保证。为此，我们采用近期提出的半定松弛技术处理格罗莫夫-沃瑟斯坦距离。数值实验验证了所提方法的有效性。
原文摘要 · Abstract (English)
This article introduces a formation shape control algorithm, in the optimal control framework, for steering an initial population of agents to a desired configuration via employing the Gromov-Wasserstein distance. The underlying dynamical system is assumed to be a constrained linear system and the objective function is a sum of quadratic control-dependent stage cost and a Gromov-Wasserstein terminal cost. The inclusion of the Gromov-Wasserstein cost transforms the resulting optimal control problem into a well-known NP-hard problem, making it both numerically demanding and difficult to solve with high accuracy. Towards that end, we employ a recent semi-definite relaxation-driven technique to tackle the Gromov-Wasserstein distance. A numerical example is provided to illustrate our results.
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