分散最適化による最小情報線形ガウス制御のスケーラブルな合成
Scalable Synthesis of Minimum-Information Linear-Gaussian Control by Distributed Optimization
状態から制御入力への有向情報量と制御コストの重み付き和を最小化するLQG制御を、時間ステップごとに分解する分散アルゴリズムで解き、ホライズン長に対して線形時間で合成できることを示した論文。障害物のある経路計画に応用し、知覚と制御のコストを同時最小化する局所最適解を数千ステップ規模で計算できる。
著者: Murat Cubuktepe, Takashi Tanaka, Ufuk Topcu
分類: eess.SY, cs.RO, cs.SY, math.OC
原文アブストラクト
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.
