# On feedback strengthening of the maximum principle for measure differential equations

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## Abstract

For a class of nonlinear nonconvex impulsive control problems with states of bounded variation driven by Borel measures, we derive a new type non-local necessary optimality condition, named impulsive feedback maximum principle. This optimality condition is expressed completely within the objects of the impulsive maximum principle (IMP), while employs certain “feedback variations” of impulsive control. The obtained optimality condition is shown to, potentially, discard non-optimal IMP-extrema, and can be viewed as a deterministic non-local iterative algorithm for optimal impulsive control.

## Keywords

Impulsive control Feedback control Control synthesis Maximum principle## Notes

### Acknowledgements

Authors are grateful to V.A. Dykhta for an inspiration of this study, and worthy advices.

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