Linear–State Control Problems and Differential Games: Deterministic and Stochastic Systems

José Márquez–Prado () and Onésimo Hernández–Lerma ()
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José Márquez–Prado: CINVESTAV–IPN
Onésimo Hernández–Lerma: CINVESTAV–IPN

Journal of Optimization Theory and Applications, 2025, vol. 205, issue 2, No 22, 37 pages

Abstract: Abstract 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 $$a(t,x) \equiv a(t)$$ 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.

Keywords: Deterministic and stochastic optimal control; Deterministic and stochastic differential games; Maximum principle; Linear-state systems; 34H05; 91A10; 91A15; 91A23; 93E20 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02657-w

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