Optimal control of threefold integrator according to minimum consumption

The solution of optimal control problem of the threefold integrator with any boundary conditions by method of moments is considered. It is shown that in case of minimization of total impulse of control influence or control consumption, the solution of $L_{\infty}$-moments problem is approximated by optimal impulse control. The general solution of the problem is obtained and the structure of optimal control is researched. The example of solution of a problem with symmetric boundary conditions is considered.