A Two-Level Computational Algorithm with Parallel Computing Capability for General Minimum-Time Control Problems

We propose a two-level computational algorithm with parallel computing capability for general minimum time control problems. The two-level approach presented in this paper is to solve a large-dimension parameter optimization problem transformed from the considered continuous mnimum-time control problem. This algorithm consists of a master and a slave programs. An efficient parallel computing scheme is developed to solve the slave program; while the master program is solved by a one dimensional gradient method. We show the convergence of this back and forth two-level algorithm. An O(1) computational complexity is achieved for each primitive iteration of the algorithm if enough arithmetic operators are available. A numerical example is presented to demonstrate the broad convergence region and the extremely fast computation of the algorithm. Furthermore, a feedback scheme based on the two level algorithm is introduced to reduce the influence of noisy enviroment and eliminate numerical imperfection appeared in the open loop computation.