On the solution of the linear time-optimal control problem with mixed constraints (Q1873557)

The paper deals with the linear time-optimal control problem subject to a mixed geometric constraint on the state variable and on the control actions. The problem investigated is reduced to the optimization problem in a Hilbert space. A class of optimization problems in a Hilbert space in which the reduced problem is embedded is considered and a general iterative method of solution is derived. A regularized algorithm which is robust to errors in the initial data is obtained. The general constructions and results are applied to the initial time-optimal control problem. Sufficient conditions for the strong convergence of the process of iterations to the set of solutions of the unperturbed time-optimal problem are given.