Abstract
AbstractThis paper is devoted to the problem of minimax optimal control problems of an extensible beam equation with distributed controls and initial velocity disturbances (or noises). The existence of optimal solutions for distributed control with fixed disturbance, namely the $(P_{v})$
(
P
v
)
problem, and the existence of minimax optimal solutions to $(P)$
(
P
)
problem without restricting the initial disturbance are proved. We derive the necessary optimality conditions for optimal solutions of the $(P_{v})$
(
P
v
)
and $(P)$
(
P
)
problems in the form of Pontryagin’s maximum principle.
Funder
National Research Foundation of Korea (NRF) grant
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory,Analysis