Eigendecomposition Parameterization of Penalty Matrices for Enhanced Control Design: Aerospace Applications
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910916915757056 |
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| author | Nurre, Nicholas P. Taheri, Ehsan |
| author_facet | Nurre, Nicholas P. Taheri, Ehsan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_16328 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Eigendecomposition Parameterization of Penalty Matrices for Enhanced Control Design: Aerospace Applications Nurre, Nicholas P. Taheri, Ehsan Optimization and Control Robotics Systems and Control 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. |
| title | Eigendecomposition Parameterization of Penalty Matrices for Enhanced Control Design: Aerospace Applications |
| topic | Optimization and Control Robotics Systems and Control |
| url | https://arxiv.org/abs/2504.16328 |