论文标题
通过磁场对非自然系统的最佳控制
Optimal Control of Nonholonomic Systems via Magnetic Fields
论文作者
论文摘要
几何最佳控制利用差异几何形状的工具来分析问题的结构，以确定控制和状态轨迹以达到预期的结果，同时最小化某些成本函数。对于受控的机械系统，该控制通常表现为外力，如果保守，可以将其添加到哈密顿量中。在这项工作中，我们专注于具有添加到符号形式的控件的机械系统上，而不是哈密顿量。实际上，这转化为控制电动系统的磁场。我们开发了一种基本理论，该理论得出了必要条件，以实现受到非独立限制的这种系统的最佳性。我们考虑了带有磁性的Chaplygin雪橇的代表性示例，其最佳控制问题是完全可集成的。
Geometric optimal control utilizes tools from differential geometry to analyze the structure of a problem to determine the control and state trajectories to reach a desired outcome while minimizing some cost function. For a controlled mechanical system, the control usually manifests as an external force which, if conservative, can be added to the Hamiltonian. In this work, we focus on mechanical systems with controls added to the symplectic form rather than the Hamiltonian. In practice, this translates to controlling the magnetic field for an electrically charged system. We develop a basic theory deriving necessary conditions for optimality of such a system subjected to nonholonomic constraints. We consider the representative example of a magnetically charged Chaplygin Sleigh, whose resulting optimal control problem is completely integrable.
