The condition number of a problem measures the sensitivity of the answer to small changes in the input, where “small” refers to some distance measure. A problem is called illconditioned if the condition number is large, and it is called ill-posed if the condition number is infinity. It is known that for many problems the (normwise) distance to the nearest ill-posed problem is proportional to th...

The main goal of our paper is to study the regularization problems which occur in predictive control of systems with severely ill-posed inverse model. We propose a new formulation of predictive control where the future controls are obtained as a solution of certain ill-posed inverse problem. This formulation leads to a possibility of closed loop on-line control of complex systems with ill-posed...