The sensitivity of computational control problems

The article discussed the sensitivity of a certain problems of linear control theory, including pole assignment, full state feedback linear quadratic control and H_∞ control. It was demonstrated that the mathematical formulation and the splitting of the problem into subproblems are essential factors in the conditioning of these problems. It was also shown that standard approaches implemented in numerical toolboxes, which present widely accepted approaches in numerical control, may face problems due to ill conditioning. Some of these problems can be avoided by reformulating the problem, but several open problems remain. To assess the accuracy of calculations and to trust numerical results, such condition and accuracy estimates should accompany computational procedures and must be included in the corresponding computer codes. Users must be aware of possible difficulties accompanying the computational process and know how to avoid them. The issues should also become an essential part of the curriculum for scientist and engineers in learning how to use and develop modern computational software.