论文标题
与输出反馈的线性随机系统的机会约束协方差控制
Chance Constrained Covariance Control for Linear Stochastic Systems With Output Feedback
论文作者
论文摘要
我们考虑了通过输出反馈转向的问题，即从初始高斯分布到具有规定的平均值和最大协方差的末端高斯分布的离散时间线性随机系统的状态分布，但要受到状态上的概率路径约束。过滤状态是通过Kalman滤波器获得的，并且就过滤状态的分布而言，该问题作为确定性凸面程序提出。我们观察到，在对状态协方差存在约束的情况下，与经典的线性二次高斯（LQG）控制相反，最佳反馈控制取决于过程噪声和观察模型。使用数值示例验证了所提出的方法的有效性。
We consider the problem of steering, via output feedback, the state distribution of a discrete-time, linear stochastic system from an initial Gaussian distribution to a terminal Gaussian distribution with prescribed mean and maximum covariance, subject to probabilistic path constraints on the state. The filtered state is obtained via a Kalman filter, and the problem is formulated as a deterministic convex program in terms of the distribution of the filtered state. We observe that, in the presence of constraints on the state covariance, and in contrast to classical Linear Quadratic Gaussian (LQG) control, the optimal feedback control depends on both the process noise and the observation model. The effectiveness of the proposed approach is verified using a numerical example.
