Methods of non-local improvement for admissible controls in linear problems with delay (Q1603121)

The authors derive formulas for improvement of the performance index for linear control problems described by ODEs with constant delay in state. Contrary to traditional variations of controls (that have a local character) used in the proof of Pontryagin's maximum principle, the formulas mentioned above give a possibility to obtain non-local improvement of admissible controls. Two illustrative examples are discussed in detail. Further construction of convergent iterative optimization methods (one of them using the projection operator) based on non-local improvement of admissible controls are described.