Numerical methods for solving minimum-time problem for linear systems

This paper offers a contemporary and comprehensive perspective on the classical algorithms utilized for the solution of minimum-time problem for linear systems (MTPLS). The use of unified notations supported by visual geometric representations serves to highlight the differences between the Neustadt-Eaton and Barr-Gilbert algorithms. Furthermore, these notations assist in the interpretation of the distance-finding algorithms utilized in the Barr-Gilbert algorithm. Additionally, we present a novel algorithm for solving MTPLS and provide a constructive proof of its convergence. Similar to the Barr-Gilbert algorithm, the novel algorithm employs distance search algorithms. The design of the novel algorithm is oriented towards solving such MTPLS for which the analytic description of the reachable set is available. To illustrate the advantages of the novel algorithm, we utilize the isotropic rocket benchmark. Numerical experiments demonstrate that, for high-precision computations, the novel algorithm outperforms others by factors of tens or hundreds and exhibits the lowest failure rate.