Optimal steering of a linear stochastic system to a final probability distribution
Optimal steering of a linear stochastic system to a final probability distribution
复制标题
线性随机系统到最终概率分布的最优控制
DOI：
--
复制
发表时间：
2014
期刊：
影响因子：
--
通讯作者：
Michele Pavon
中科院分区：
文献类型：
--
作者：
Yongxin Chen;T. Georgiou;Michele Pavon
我们考虑的问题，引导一个线性动力系统与完整的状态观测，从一个初始的高斯分布在状态空间中的最终一个最小能量控制。该系统是随机驱动通过控制通道，这样的系统的一个例子是，一个惯性粒子经历随机的“白色噪声“强迫。我们表明，目标概率分布总是可以在有限的时间内实现。最优控制的状态反馈形式，并计算显式求解微分李雅普诺夫方程，通过其边界值耦合。这一结果，由于其有吸引力的算法性质，似乎有几个潜在的应用，如主动控制纳米机械系统和分子冷却。控制端点边缘之间的扩散过程的问题有很长的历史（Schr\“odinger桥），因此，控制线性随机系统的当前情况构成了可能退化扩散的Schr\“odinger桥.然而，我们的结果，提供了第一个可实现的形式的一般高斯-马尔可夫过程的最优控制。惯性粒子和随机振荡器的最优演化和控制的说明性例子。最后的结果直接建立了薛定谔桥的属性作为最可能的随机演化之间的给定的边缘到目前的线性随机系统的背景。
We consider the problem to steer a linear dynamical system with full state observation from an initial gaussian distribution in state-space to a final one with minimum energy control. The system is stochastically driven through the control channels; an example for such a system is that of an inertial particle experiencing random"white noise"forcing. We show that a target probability distribution can always be achieved in finite time. The optimal control is given in state-feedback form and is computed explicitely by solving a pair of differential Lyapunov equations that are coupled through their boundary values. This result, given its attractive algorithmic nature, appears to have several potential applications such as to active control of nanomechanical systems and molecular cooling. The problem to steer a diffusion process between end-point marginals has a long history (Schr\"odinger bridges) and therefore, the present case of steering a linear stochastic system constitutes a Schr\"odinger bridge for possibly degenerate diffusions. Our results, however, provide the first implementable form of the optimal control for a general Gauss-Markov process. Illustrative examples of the optimal evolution and control for inertial particles and a stochastic oscillator are provided. A final result establishes directly the property of Schr\"{o}dinger bridges as the most likely random evolution between given marginals to the present context of linear stochastic systems.
线性系统的随机桥
影响因子：
6.8
作者：
Chen, Yongxin;Georgiou, Tryphon
通讯作者：
Georgiou, Tryphon