Metric Regularity Properties in Bang-Bang Type Linear-Quadratic Optimal Control Problems
| Autor: | Teresa Scarinci, Vladimir M. Veliov, Jakob Preininger |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Statistics and Probability
Bang-bang controls Newton’s method 0211 other engineering and technologies Control variable 010103 numerical & computational mathematics 02 engineering and technology 01 natural sciences Convexity Metric regularity Quadratic equation Applied mathematics 0101 mathematics Mathematics Numerical Analysis 021103 operations research Smoothness (probability theory) Applied Mathematics Stability analysis Linear control systems Lipschitz continuity Optimal control Variational analysis Metric (mathematics) Geometry and Topology Affine transformation Analysis |
| Popis: | The paper investigates the Lipschitz/Holder stability with respect to perturbations of optimal control problems with linear dynamic and cost functional which is quadratic in the state and linear in the control variable. The optimal control is assumed to be of bang-bang type and the problem to enjoy certain convexity properties. Conditions for bi-metric regularity and (Holder) metric sub-regularity are established, involving only the order of the zeros of the associated switching function and smoothness of the data. These results provide a basis for the investigation of various approximation methods. They are utilized in this paper for the convergence analysis of a Newton-type method applied to optimal control problems which are affine with respect to the control. |
| Databáze: | OpenAIRE |
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