论文标题
基于分配距离终端成本的离散时间随机线性系统的协方差转向
Covariance Steering of Discrete-Time Stochastic Linear Systems Based on Distribution Distance Terminal Costs
论文作者
论文摘要
我们考虑了离散时间随机线性系统的一类随机最佳控制问题，该系统寻求控制策略，这些控制策略将引导系统的末端状态的概率分布，接近所需的高斯分布。在我们的问题制定中，终端状态分布与所需（目标）分布之间的接近度是根据平方的瓦斯坦距离来衡量的，该距离与相应的终端成本项有关。我们将随机最佳控制问题重新铸造为有限维非线性程序，我们表明其性能指数可以表示为两个凸功能的差异。性能索引的这种表示使我们能够通过所谓的凸孔程序找到原始非线性程序的本地最小化器[1]。随后，我们考虑了一个类似的问题，但是这次我们使用与KL Divergence相对应的终端成本。最后，我们提出了非平凡的数值模拟，以证明所提出的技术并在计算时间上进行比较。
We consider a class of stochastic optimal control problems for discrete-time stochastic linear systems which seek for control policies that will steer the probability distribution of the terminal state of the system close to a desired Gaussian distribution. In our problem formulation, the closeness between the terminal state distribution and the desired (goal) distribution is measured in terms of the squared Wasserstein distance which is associated with a corresponding terminal cost term. We recast the stochastic optimal control problem as a finite-dimensional nonlinear program and we show that its performance index can be expressed as the difference of two convex functions. This representation of the performance index allows us to find local minimizers of the original nonlinear program via the so-called convex-concave procedure [1]. Subsequently, we consider a similar problem but this time we use a terminal cost that corresponds to the KL divergence. Finally, we present non-trivial numerical simulations to demonstrate the proposed techniques and compare them in terms of computation time.
