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Linear–State Control Problems and Differential Games: Deterministic and Stochastic Systems
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Linear–State Control Problems and Differential Games: Deterministic and Stochastic Systems
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Journal Article
Linear–State Control Problems and Differential Games: Deterministic and Stochastic Systems
2025
Overview
This paper concerns a class of
linear-state
optimal control problems and noncooperative differential games. Deterministic and stochastic systems are considered, as well as finite- and infinite-horizon problems. We give conditions under which these systems have
degenerate
feedback optimal controls so that the optimal control actions
a
(
t
,
x
)
≡
a
(
t
)
are independent of the state variable
x
. As a consequence, open-loop and feedback (or Markov) optimal controls coincide, the value (or optimal objective) function is linear in the state
x
, and the
certainty equivalence
principle is satisfied.
Publisher
Springer US,Springer Nature B.V
