Sequential synthesis of time optimal control by a linear system with disturbance

A method of sequential synthesis of time optimal control by a linear system with unknown disturbance is con-sidered. A simple way of forming in real time a piecewise con-stant finite control moving a linear system from an initial state to the origin is proposed,the approximate solution to speed problem being provided. The relations are obtained that transform sequence of the finite controls to time optimal control. The evaluations consist in solving repeatedly the system of linear algebraic equations and integrating the mat-rix differential equation on the displacement intervals of the control switching times and that of the final control time. The simple and constructive conditions are obtained for: occurrence of discontinuous mode; moving the representative point along the switching manifolds; transformation of the optimal control structure in moving the phase trajectory of the system with uncontrollable disturbance.The method is evaluated in terms of its computational burden and the procedure of setting initial approximation that substantially decreases it is examined. The computational algorithm is given. Sequence of the controls is proved to converge to optimal control.