论文标题
基于仿射干扰反馈控制参数化的最小差异和协方差转向
Minimum Variance and Covariance Steering Based on Affine Disturbance Feedback Control Parameterization
论文作者
论文摘要
本文的目的是解决有限的 - 摩尼斯最小方差和协方差转向问题，以解决离散时间随机（高斯）线性系统。一方面，最小差异问题寻求控制策略，该政策将使不确定系统的状态转移到规定数量的同时，同时最大程度地减少其终端国家协方差（或差异）的痕迹。另一方面，协方差转向问题寻求一项控制政策，该政策将把终端国家的协方差转向处方的正定矩阵。我们提出了一种依赖于仿射干扰反馈控制参数的随机版本的解决方案方法，每个阶段的控制输入可以表示为在系统上作用的干扰历史的仿射功能。我们的分析表明，这种特定的参数允许人们将本文所考虑的随机最佳控制问题减少到具有基本相同决策变量的可拖动凸面程序中。这与其他控制策略参数相反，例如状态反馈参数化，其中凸面程序的决策变量与随机最佳控制问题的控制器参数不一致。此外，我们提出了控制参数化的变化，该变化依赖于过去干扰的截断历史。我们表明，通过适当地选择截断序列的长度，我们可以设计次优控制器，这可以在性能和计算成本之间取得所需的平衡。
The goal of this paper is to address finite-horizon minimum variance and covariance steering problems for discrete-time stochastic (Gaussian) linear systems. On the one hand, the minimum variance problem seeks for a control policy that will steer the state mean of an uncertain system to a prescribed quantity while minimizing the trace of its terminal state covariance (or variance). On the other hand, the covariance steering problem seeks for a control policy that will steer the covariance of the terminal state to a prescribed positive definite matrix. We propose a solution approach that relies on the stochastic version of the affine disturbance feedback control parametrization according to which the control input at each stage can be expressed as an affine function of the history of disturbances that have acted upon the system. Our analysis reveals that this particular parametrization allows one to reduce the stochastic optimal control problems considered herein into tractable convex programs with essentially the same decision variables. This is in contrast with other control policy parametrizations, such as the state feedback parametrization, in which the decision variables of the convex program do not coincide with the controller's parameters of the stochastic optimal control problem. In addition, we propose a variation of the control parametrization which relies on truncated histories of past disturbances. We show that by selecting the length of the truncated sequences appropriately, we can design suboptimal controllers which can strike the desired balance between performance and computational cost.
