時間スケーリングを伴う線形および区分アフィン最適制御のための新しい半正定値緩和
A New Semidefinite Relaxation for Linear and Piecewise-Affine Optimal Control with Time Scaling
時間スケーリングを含む線形・区分アフィン系の最適制御問題に対し、計算負荷を抑えつつタイトな半正定値緩和を提案し、単一の半正定値計画問題として解く手法を開発した。
詳しい要約
1. どんなもの？
2. 先行研究と比べてどこがすごい？
3. 技術・手法の肝は？
4. どうやって有効だと検証した？
5. 議論はある？
6. 次に読むべき論文は？
※ AIが要旨から生成した要約です。正確性は原文をご確認ください。
著者: Lujie Yang, Tobia Marcucci, Pablo A. Parrilo, Russ Tedrake
分類: cs.RO, cs.SY, eess.SY, math.OC
原文アブストラクト
We introduce a semidefinite relaxation for optimal control of linear systems with time scaling. These problems are inherently nonconvex, since the system dynamics involves bilinear products between the discretization time step and the system state and controls. The proposed relaxation is closely related to the standard second-order semidefinite relaxation for quadratic constraints, but we carefully select a subset of the possible bilinear terms and apply a change of variables to achieve empirically tight relaxations while keeping the computational load light. We further extend our method to handle piecewise-affine (PWA) systems by formulating the PWA optimal-control problem as a shortest-path problem in a graph of convex sets (GCS). In this GCS, different paths represent different mode sequences for the PWA system, and the convex sets model the relaxed dynamics within each mode. By combining a tight convex relaxation of the GCS problem with our semidefinite relaxation with time scaling, we can solve PWA optimal-control problems through a single semidefinite program.
