Non-degenerate maximum principle for optimal control problems with discontinuous right-hand side

ABSTRACT

In the paper, optimal control problems with discontinuous right-hand side are considered. The main attention is paid to situations when there are intervals where optimal trajectory lies on a switching surface. It is shown that for such a situation the known optimality conditions degenerate: they are satisfied for any feasible control. Hence such conditions are not informative. New non-degenerate necessary optimality conditions in a form of Maximum principle are formulated and proved. Comparison of the obtained optimality conditions with ones known from the literature is presented.

KEYWORDS:

• Optimal control
• systems with discontinuous right-hand side
• optimality conditions

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 Such partitioning is not unique. Further we consider the partitioning of the set ${\mathcal{T}}_k$ with minimal number $p\left(k\right)$.

Additional information

Funding

The publication has been prepared with the support of the State Research Program ‘Convergence’(Republic Belarus) [Task 1.3.01] and with the support of the RUDN University Program 5-100 [02.a03.21.0008].