论文标题
对谎言组的多种系统最佳控制的对称性减少
Symmetry Reduction in Optimal Control of Multiagent Systems on Lie Groups
论文作者
论文摘要
我们研究了方程的降低，这些方程式通过利用代理的物理对称性来确定超级控制问题的必要最佳条件，在这种方程式中，每个药物的运动学的物理对称性是由左右不变的控制系统给出的。使用变异微积分和拉格朗日力学的技术可获得降低的最佳条件。还研究了哈密顿的形式主义，其中通过应用庞特氏素的最大原理来探索问题，并作为减少汉密尔顿载体场的积分曲线获得了最佳条件。我们将结果应用于多个独轮车的能量最小控制问题。
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.
