论文标题
通过Wasserstein终端成本进行离散时间协方差转向的确切的SDP公式
Exact SDP Formulation for Discrete-Time Covariance Steering with Wasserstein Terminal Cost
论文作者
论文摘要
在本文中，我们介绍了Wasserstein距离终端成本的协方差转向问题的新结果。我们表明，在解决此类问题之前已使用的状态历史反馈控制策略参数化需要不必要的变量，并且可以用随机状态反馈策略代替，这会导致更易于触发的问题表述，而不会出现任何绩效损失。特别是，我们表明，在后一种策略下，该问题可以等效地作为半明确计划（SDP），这与我们先前的结果形成鲜明对比，这只能保证可以将随机最佳控制问题降低到cosvex函数程序的差异。然后，我们表明，通过求解相关的SDP找到的最佳策略对应于确定性的状态反馈策略。最后，我们提出了非平凡的数值模拟，该模拟显示了我们提出的随机状态反馈策略的好处，该策略从问题的SDP公式中，就计算效率和控制器性能而言，与现有方法相比现有方法。
In this paper, we present new results on the covariance steering problem with Wasserstein distance terminal cost. We show that the state history feedback control policy parametrization, which has been used before to solve this class of problems, requires an unnecessarily large number of variables and can be replaced by a randomized state feedback policy which leads to more tractable problem formulations without any performance loss. In particular, we show that under the latter policy, the problem can be equivalently formulated as a semi-definite program (SDP) which is in sharp contrast with our previous results that could only guarantee that the stochastic optimal control problem can be reduced to a difference of convex functions program. Then, we show that the optimal policy that is found by solving the associated SDP corresponds to a deterministic state feedback policy. Finally, we present non-trivial numerical simulations which show the benefits of our proposed randomized state feedback policy derived from the SDP formulation of the problem over existing approaches in the field in terms of computational efficacy and controller performance.
