固有値分解によるペナルティ行列パラメータ化と制御設計の高度化：航空宇宙応用
Eigendecomposition Parameterization of Penalty Matrices for Enhanced Control Design: Aerospace Applications
制御則の重み行列を固有値分解でパラメータ化し、非対角成分を許容することで性能を最大65%改善する手法を提案し、宇宙機の姿勢制御や軌道設計に適用した。
著者: Nicholas P. Nurre, Ehsan Taheri
分類: math.OC, cs.RO, cs.SY, eess.SY
原文アブストラクト
Modern control algorithms require tuning of square weight/penalty matrices appearing in quadratic functions/costs to improve performance and/or stability output. Due to simplicity in gain-tuning and enforcing positive-definiteness, diagonal penalty matrices are used extensively in control methods such as linear quadratic regulator (LQR), model predictive control, and Lyapunov-based control. In this paper, we propose an eigendecomposition approach to parameterize penalty matrices, allowing positive-definiteness with non-zero off-diagonal entries to be implicitly satisfied, which not only offers notable computational and implementation advantages, but broadens the class of achievable controls. We solve three control problems: 1) a variation of Zermelo's navigation problem, 2) minimum-energy spacecraft attitude control using both LQR and Lyapunov-based methods, and 3) minimum-fuel and minimum-time Lyapunov-based low-thrust trajectory design. Particle swarm optimization is used to optimize the decision variables, which will parameterize the penalty matrices. The results demonstrate improvements of up to 65% in the performance objective in the example problems utilizing the proposed method.
