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arXiv · 2504.16328

Eigendecomposition Parameterization of Penalty Matrices for Enhanced Control Design: Aerospace Applications

Nicholas P. Nurre·Ehsan Taheri
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Abstract

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.

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Nicholas P. Nurre, Ehsan Taheri. 2025-04-23. Eigendecomposition Parameterization of Penalty Matrices for Enhanced Control Design: Aerospace Applications. https://arxiv.org/abs/2504.16328

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