A problem of best approximation of linear systems for a chosen class of controls. (Polish. English summary) Zbl 0572.93032
A problem of best approximation of linear systems for all control signals belonging to a chosen class of functions is considered. The norm of the difference of the outputs of two systems for the most dangerous control from the given class is the criterion of approximation of one of these systems by the other. The best approximation is obtained by means of the minimization of this criterion with respect to the parameters of the approximating system. Thus, the obtained accuracy is guaranteed for all controls even for the worst one. Two numerical examples for two different classes of controls are presented.
MSC:
| 93C05 | Linear systems in control theory |
| 41A50 | Best approximation, Chebyshev systems |
| 49J15 | Existence theories for optimal control problems involving ordinary differential equations |
| 49J30 | Existence of optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) |
