Finite horizon linear quadratic Gaussian density regulator with Wasserstein terminal cost
Finite horizon linear quadratic Gaussian density regulator with Wasserstein terminal cost
复制标题
具有 Wasserstein 终端成本的有限水平线性二次高斯密度调节器
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
Eric D. B. Wendel
中科院分区：
文献类型：
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作者：
A. Halder;Eric D. B. Wendel
我们制定并解决了一个最优控制问题，其中有限维线性时不变（LTI）控制系统在固定时间内将给定的高斯概率密度函数（PDF）转向另一个高斯概率密度函数，同时最小化轨迹期望二次代价。我们用两个密度函数之间的Wasserstein距离的平方来衡量实际终端PDF和期望终端PDF之间的“亲密度”，并以终端成本来惩罚缺乏亲密度。我们发现与标准线性二次高斯（LQG）控制问题不同，所得到的线性二次高斯密度调节器的必要条件导致协方差Lyapunov矩阵微分方程和协方差协态Riccati矩阵微分方程的边界条件之间的非线性耦合。我们证明了LQG控制问题可以作为我们的密度调节器问题的一个特例来恢复，并通过一个数值例子说明了我们的公式。
We formulate and solve an optimal control problem in which a finite dimensional linear time invariant (LTI) control system steers a given Gaussian probability density function (PDF) close to another in fixed time, while minimizing the trajectory-wise expected quadratic cost. We measure the “closeness” between the actual terminal PDF and the desired terminal PDF as the squared Wasserstein distance between the two density functions, and penalize the lack of closeness as terminal cost. We find that unlike the standard linear quadratic Gaussian (LQG) control problem, the necessary conditions for the resulting linear quadratic Gaussian density regulator lead to nonlinear coupling between the boundary conditions of the covariance Lyapunov matrix differential equation and the covariance costate Riccati matrix differential equation. We show that the LQG control problem can be recovered as a special case of our density regulator problem, and illustrate our formulation on a numerical example.
影响因子：
6.8
作者：
Chen, Yongxin;Georgiou, Tryphon T.;Pavon, Michele
通讯作者：
Pavon, Michele