Optimal synthesis in the simplest time-optimal problem with a linear state constraint

Abstract

We consider the time-optimal problem for a classical system of "double integrator" under the presence of a linear state constraint. By using the Maximum Principle of Dubovitskii and Milyutin, we determine a complete synthesis of optimal trajectories and qualitatively analyze the corresponding Lagrange multipliers.

arXiv comment27 pages, 9 figures