论文标题
通过分布式优化对最小信息线性控制的最小信息控制的合成
Scalable Synthesis of Minimum-Information Linear-Gaussian Control by Distributed Optimization
论文作者
论文摘要
我们考虑一个离散的时间线性季度高斯控制问题，其中我们将从系统状态到控制输入和控制成本的有向信息的加权总和最小化。可以通过解决半决赛编程问题共同合成最佳控制和传感策略。但是，现有的解决方案通常以地平线长度扩展立方体。我们利用问题中的结构来开发一种分布式算法，该算法将合成问题分解为一组较小的问题，每个时间步长一个。我们证明该算法在时间线性上以地平线长度线性运行。作为算法的应用，我们考虑了在存在随机干扰存在下障碍物的状态空间中的路径规划问题。该算法计算了本地最佳解决方案，该解决方案共同最大程度地减少了感知和控制成本，同时确保路径的安全性。数值示例表明，该算法可以扩展到数千个地平线长度并计算本地最佳解决方案。
We consider a discrete-time linear-quadratic Gaussian control problem in which we minimize a weighted sum of the directed information from the state of the system to the control input and the control cost. The optimal control and sensing policies can be synthesized jointly by solving a semidefinite programming problem. However, the existing solutions typically scale cubic with the horizon length. We leverage the structure in the problem to develop a distributed algorithm that decomposes the synthesis problem into a set of smaller problems, one for each time step. We prove that the algorithm runs in time linear in the horizon length. As an application of the algorithm, we consider a path-planning problem in a state space with obstacles under the presence of stochastic disturbances. The algorithm computes a locally optimal solution that jointly minimizes the perception and control cost while ensuring the safety of the path. The numerical examples show that the algorithm can scale to thousands of horizon length and compute locally optimal solutions.
