Regularization Method for Ill-Posed Non-Singular Linear Time-Invariant Time-Optimal Regulator Problem

Regularization method is investigated for ill-posed non-singular linear time-optimal regulator problem. The regularization algorithm to construct the minimizing control sequence which converges to its optimal value is presented. It has been shown that the minimizing sequence constructed base upon the regularizing operator and smoothing functional is converging to optimal control u* where u* is an element of a "complete" m dimensional metric space.