Optimal covariance control for stochastic linear systems subject to integral quadratic state constraints
Optimal covariance control for stochastic linear systems subject to integral quadratic state constraints
复制标题
受积分二次状态约束的随机线性系统的最优协方差控制
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
E. Bakolas
中科院分区：
文献类型：
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作者：
E. Bakolas
本文研究了二次状态积分约束下随机线性系统的最优协方差控制问题。特别是，我们的目标是设计一个反馈控制律，将引导的协方差矩阵的（随机）终端状态向量的随机线性系统的一个指定的半正定矩阵，同时最小化的期望值的控制所需的努力，这个“协方差转换”或“薛定谔桥”的积分二次状态不等式约束。我们解决这个问题，通过将其嵌入到一个参数家庭的无约束协方差控制问题，更容易处理，无论是分析和计算，比原来的，有约束的协方差控制问题。通过这种方式，原来的问题基本上是减少到一个有限维的最优参数选择问题，这可以通过梯度下降型算法来解决。
This work is concerned with an optimal covariance control problem for stochastic linear systems subject to quadratic state integral constraints. In particular, our objective is to design a feedback control law that will steer the covariance matrix of the (random) terminal state vector of a stochastic linear system to a designated positive semi-definite matrix while minimizing the expected value of the control effort required for this “covariance transition” or “Schrödinger bridge” subject to integral quadratic state inequality constraints. We address this problem by imbedding it into a one-parameter family of unconstrained covariance control problems that are more tractable, both analytically and computationally, than the original, constrained covariance control problem. In this way, the original problem is essentially reduced to a finite-dimensional optimal parameter selection problem, which can be addressed by means of gradient descent-type algorithms.