李群上多智能体系统最优控制的对称约化
Symmetry Reduction in Optimal Control of Multiagent Systems on Lie Groups
摘要：
我们研究减少自由度的方程，确定必要的最优性条件极值的最优控制问题的多智能体系统，通过利用代理的物理对称性，其中每个代理的运动学是由一个左不变的控制系统。减少最优性条件得到使用变分法和拉格朗日力学的技术。一个哈密顿形式主义也进行了研究，通过应用庞特里亚金的最大值原理左不变系统的问题进行了探讨，和最优性条件得到的积分曲线的约化哈密顿向量场。我们将结果应用到多个单轮车的能量最小控制问题。
英文摘要：
We study the reduction of degrees of freedom for the equations that determine necessary optimality conditions for extrema in an optimal control problem for a multiagent system by exploiting the physical symmetries of agents, where the kinematics of each agent is given by a left-invariant control system. Reduced optimality conditions are obtained using techniques from variational calculus and Lagrangian mechanics. A Hamiltonian formalism is also studied, where the problem is explored through an application of Pontryagin's maximum principle for left-invariant systems, and the optimality conditions are obtained as integral curves of a reduced Hamiltonian vector field. We apply the results to an energy-minimum control problem for multiple unicycles.
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