Stochastic linear systems subject to constraints
Stochastic linear systems subject to constraints
复制标题
受约束的随机线性系统
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
本文在完全状态信息的假设下，研究了具有平均和约束的随机离散线性系统的最优协方差控制问题，该约束涉及状态和控制输入序列的二次函数。我们表明，随机最优控制问题是一个确定性的非线性规划，其中，根据明智的选择的决策变量，可以带来的形式，其性能指标是一个凸的，二次函数受到平等和不平等的二次约束。这里的关键挑战源于这样一个事实，即由状态协方差上的终端约束产生的等式约束可能不一定是凸的。然而，我们表明，通过采用一个简单的松弛技术，非线性规划与凸规划，这可以通过强大的和有效的算法来解决。尽管松弛凸规划的解不一定会给出其端点完全遵循目标高斯分布的闭环轨迹，但预计此类轨迹的代表性样本的端点将比从目标高斯分布绘制的端点更集中在原点附近。最后，数值模拟说明了一些关键的想法，本文。
This work deals with an optimal covariance control problem for stochastic discrete-time linear systems subject to mean sum constraints involving quadratic functions of the state and the control input sequences under the assumption of full state information. We show that the stochastic optimal control problem is equivalent to a deterministic nonlinear program, which, under a judicious choice of the decision variable, can be brought to a form in which its performance index is a convex, quadratic function subject to both equality and inequality quadratic constraints. The key challenge here stems from the fact that the equality constraints that result from the terminal constraints on the state covariance may not be necessarily convex. We show, however, that by employing a simple relaxation technique, the nonlinear program is associated with a convex program, which can be addressed by means of robust and efficient algorithms. Despite the fact that the solution to the relaxed convex program will not necessarily give closed-loop trajectories whose endpoints follow exactly the goal Gaussian distribution, a representative sample of such trajectories are expected to have endpoints that will be more concentrated near the origin than if there were drawn from the goal Gaussian distribution. Finally, numerical simulations that illustrate some key ideas of the paper are presented.
影响因子：
6.8
作者：
Chen, Yongxin;Georgiou, Tryphon T.;Pavon, Michele
通讯作者：
Pavon, Michele