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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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