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The time-optimal control problem for the system ˙ x 1 = u, ˙ x 2 = x 1 , ˙ x 3 = x 3 1 is considered. Explicit formulas for nding optimal controls are given. The explicit solution of the optimal synthesis problem is obtained.fatcat:nz5ggfj6z5hhxms44ox4gvnjbq