论文标题
基于无香的转换，用于离散时间随机非线性系统的贪婪有限摩尼克协方差转向
Greedy Finite-Horizon Covariance Steering for Discrete-Time Stochastic Nonlinear Systems Based on the Unscented Transform
论文作者
论文摘要
在这项工作中，我们考虑了转向离散时间非线性随机系统不确定状态的前两个时刻的问题，以便在给定的最后时间规定目标数量。原则上，后一个问题可以作为密度跟踪问题提出，该问题寻求反馈策略，该策略将使系统状态的概率密度函数（就适当的度量标准而言）保持在目标密度上。但是，解决后一种无限维度问题的解决方案可能是一项复杂且计算昂贵的任务。取而代之的是，我们提出了一种依赖贪婪控制政策的更容易易加和直观的方法。后一种控制策略由控制策略的第一元素组成，该策略解决了相应的线性化协方差转向问题。这些协方差转向问题中的每一个仅依赖于当前阶段的国家均值和国家协方差的信息，并且可以作为易于处理的（有限维）凸面程序进行配合。在每个阶段，通过计算下一阶段的预测状态均值和协方差的近似值来更新有关状态统计信息的信息。还提出了说明我们方法关键思想的数值模拟。
In this work, we consider the problem of steering the first two moments of the uncertain state of a discrete time nonlinear stochastic system to prescribed goal quantities at a given final time. In principle, the latter problem can be formulated as a density tracking problem, which seeks for a feedback policy that will keep the probability density function of the state of the system close, in terms of an appropriate metric, to the goal density. The solution to the latter infinite-dimensional problem can be, however, a complex and computationally expensive task. Instead, we propose a more tractable and intuitive approach which relies on a greedy control policy. The latter control policy is comprised of the first elements of the control policies that solve a sequence of corresponding linearized covariance steering problems. Each of these covariance steering problems relies only on information available about the state mean and state covariance at the current stage and can be formulated as a tractable (finite-dimensional) convex program. At each stage, the information on the state statistics is updated by computing approximations of the predicted state mean and covariance of the resulting closed-loop nonlinear system at the next stage by utilizing the (scaled) unscented transform. Numerical simulations that illustrate the key ideas of our approach are also presented.
