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An Algebraic Method for Optimizing the State, Control, and Terminal State Weight Matrices for Optimal Feedback Control — arXiv:2608.12702

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.12702
License (as archived): CC0-1.0
Archived: 2026-10-19T04:46:22.666Z
SHA-256 of the archived text: 46c02a964dbd1431c0de640d03f7c6a1beb777abea32194d6245f53bce156fd9
Stable URL of this page: https://metraipolis.com/documento/dc_0ce2277ff005

How to cite

An Algebraic Method for Optimizing the State, Control, and Terminal State Weight Matrices for Optimal Feedback Control — arXiv:2608.12702 — arXiv (en), https://arxiv.org/abs/2608.12702 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_0ce2277ff005 (Metraipolis archive dc_0ce2277ff005, sha256 46c02a964dbd1431c0de640d03f7c6a1beb777abea32194d6245f53bce156fd9)

BibTeX

@misc{dc0ce2277ff005,
  title = {An Algebraic Method for Optimizing the State, Control, and Terminal State Weight Matrices for Optimal Feedback Control — arXiv:2608.12702},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.12702},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_0ce2277ff005; sha256 46c02a964dbd1431c0de640d03f7c6a1beb777abea32194d6245f53bce156fd9},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.12702. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

The necessary conditions for formulating optimal feedback control algorithms have been known for many years. Free parameters exist in the performance index in the form of state and control penalty and terminal state penalty matrices for tuning the performance of the optimally controlled system. The selection process is typically experimental and iterative. To generate the weight matrices for optimal feedback control algorithms, an optimization process is proposed. Typically, the optimization process for the weight matrices requires several numerical integration processes that are computationally expensive; this work overcomes the classical high computational cost by exploiting closed-form solutions for the time-varying Riccati matrix, state trajectories, state transition matrix, and the optimal performance index. Closed-form algebraic equations are used to generate all partial derivative calculations, and no numerical integration is required. The closed-form partial derivatives are used to generate analytic gradients for the optimization steps. The optimization strategy seeks to minimize the terminal state values for the feedback control problem. A numerical example is presented to demonstrate the effectiveness of the proposed optimization algorithm. The resulting computational procedures are expected to be broadly useful for control theory applications in science and engineering.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-08-14 in math.OC).
Categorie arXiv: Optimization and Control (math.OC).
Pagina del lavoro: https://arxiv.org/abs/2608.12702 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-19T04:27:11.018Z dalla pagina https://arxiv.org/catchup/math.OC/2026-08-14?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).