Neighborhood of the Second-Order Singular Regime in Problems with Control in a Disk

M. I. Ronzhina ; L. A. Manita ; L. V. Lokutsievskiy

Informatics and Automation, Optimal Control and Differential Games, Tome 315 (2021), pp. 222-236.

Résumé

We consider Hamiltonian systems that are affine in a two-dimensional control with values in a disk. In the neighborhood of a second-order singular extremal, we study the structure of optimal synthesis and find a family of solutions in the form of logarithmic spirals that make countably many revolutions around a singular point and reach this point in finite time.

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