Numerical solution for linear time optimal control problem

We obtain the system of linear algebraic equations connecting the differences of initial conditions for normalized conjugate system and the difference of time of process completion with those of phase coordinates of controlled system. The quasioptimal control being some piecewise continuous approximation to required optimal control is used to ensure the moving of the system from a defined initial state to the origin for fixed time. The computing process and the sequence of quasioptimal controls have been proved to converge to optimal control. The radius with quadratic speed of convergence has been found. The procedure of minimization of iteration number has been considered.