A Primal-Dual Method for Optimal Control and Trajectory Generation in High-Dimensional Systems
A Primal-Dual Method for Optimal Control and Trajectory Generation in High-Dimensional Systems
复制标题
高维系统最优控制和轨迹生成的原对偶方法
DOI：
10.1109/ccta.2018.8511584
复制
发表时间：
2017
期刊：
影响因子：
--
通讯作者：
S. Osher
中科院分区：
文献类型：
--
作者：
Matthew R. Kirchner;G. Hewer;J. Darbon;S. Osher
提出了一种利用广义Hopf公式求解时间最优控制问题的Hamilton-Jacobi（HJ）方程的有效方法。通常，求解HJ方程的数值方法依赖于解空间的离散网格，并表现出随维度的指数缩放。广义霍普夫公式避免了使用网格和数值梯度，制定一个无约束的凸优化问题。每个点的解决方案是完全独立的，如果需要多个点的解决方案，则允许大规模并行实现。这项工作提出了一种原始-对偶方法，有效的数值解，并提出了如何产生的最佳轨迹可以直接从解决方案的霍普夫公式，没有进一步的优化。所提出的示例具有毫秒级的执行时间，并且实验显示计算尺度近似为多项式，具有非常小的高阶系数。
Presented is a method for efficient computation of the Hamilton-Jacobi (HJ) equation for time-optimal control problems using the generalized Hopf formula. Typically, numerical methods to solve the HJ equation rely on a discrete grid of the solution space and exhibit exponential scaling with dimension. The generalized Hopf formula avoids the use of grids and numerical gradients by formulating an unconstrained convex optimization problem. The solution at each point is completely independent, and allows a massively parallel implementation if solutions at multiple points are desired. This work presents a primal-dual method for efficient numeric solution and presents how the resulting optimal trajectory can be generated directly from the solution of the Hopf formula, without further optimization. Examples presented have execution times on the order of milliseconds and experiments show computation scales approximately polynomial in dimension with very small high-order coefficients.
影响因子：
3.1
作者：
Al-Mohy, Awad H.;Higham, Nicholas J.
通讯作者：
Higham, Nicholas J.