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Numerical methods for solving minimum-time problem for linear systems

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  • Buzikov, Maksim
  • Mayer, Alina

Abstract

This paper presents a novel algorithm for solving minimum-time problem for linear systems (MTPLS) and offers a contemporary perspective on well-known classical algorithms. The use of unified notations supported by visual geometric representations serves to highlight the differences between the most famous algorithms: Neustadt-Eaton and Barr-Gilbert algorithms. Additionally, we provide a constructive proof of convergence of the new algorithm, which fills a gap in the constructiveness of the step-size selection of the Neustadt-Eaton algorithm. The novel algorithm is designed to solve MTPLS problems for which an analytic description of the reachable set is available. The study's importance lies in its ability to provide mathematical guarantees of correctness for the numerical computation of optimal solutions for a broad class of MTPLS. We utilize the isotropic rocket benchmark to illustrate the advantages of the novel algorithm. Numerical experiments demonstrate that for high-precision calculations it exhibits the highest computational speed and the lowest failure rate.

Suggested Citation

  • Buzikov, Maksim & Mayer, Alina, 2026. "Numerical methods for solving minimum-time problem for linear systems," Applied Mathematics and Computation, Elsevier, vol. 508(C).
    • Handle: RePEc:eee:apmaco:v:508:y:2026:i:c:s0096300325003601
    DOI: 10.1016/j.amc.2025.129634
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    References listed on IDEAS

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    1. Efstathios Bakolas & Panagiotis Tsiotras, 2013. "Optimal Synthesis of the Zermelo–Markov–Dubins Problem in a Constant Drift Field," Journal of Optimization Theory and Applications, Springer, vol. 156(2), pages 469-492, February.
    2. Efstathios Bakolas, 2014. "Optimal Guidance of the Isotropic Rocket in the Presence of Wind," Journal of Optimization Theory and Applications, Springer, vol. 162(3), pages 954-974, September.
    3. Xiaolong Qin & Nguyen Thai An, 2019. "Smoothing algorithms for computing the projection onto a Minkowski sum of convex sets," Computational Optimization and Applications, Springer, vol. 74(3), pages 821-850, December.
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