Iterative method for computing time optimal control in real time mode

We propose a simple method for forming a piecewise constant finite control in the real-time mode, which transfers a linear system from any initial state to the origin in a fixed time. The relations for a sequence of finite controls to be transformed into the fast time optimal control are obtained. Computations are carried out while the system is monitored. The iterative process of computing the optimal control reduces to a sequence of solutions to linear algebraic equations and the Cauchy problems. Effective techniques for setting an initial approximation are proposed, which significantly decrease the number of iterations. A sequence of finite controls is proved to converge to the time optimal control. Results of modeling and computing are given.