Computational solution of time-optimal control problem for linear systems with delay

A computational method of solving time-optimal control problem for linear systems with delay is proposed. It is proved that the method converges in a finite number of iterations to an $\varepsilon$-optimal solution, which is understood as a pair $\{T,u\},$ where $u=u(t)$, $t\in[0,T]$ is an admissible control that moves the system into an $\varepsilon$-neighborhood of the origin in time $T\le T_{\min}$, and the optimal time is $T_{\min}$. An enough general time-optimal control problem with delay is studied in [Vasil'ev F. P, Ivanov R. P. On an approximated solving of time-optimal control problem with delay, Zh. Vychisl. Mat. Mat. Fiz., 1970, vol. 10, no. 5, pp. 1124–1140 (in Russian)], an approximate solution is proposed for it, and computational aspects are discussed. However, to solve some auxiliary optimal control problems arising there, it is suggested to use methods of gradient and Newton type, which possess only a local convergence. The method proposed in the present paper has a global convergence.