In this section
@article{Astolfi:2026:10.1080/00207721.2026.2672127,
author = {Astolfi, A and Sassano, M},
doi = {10.1080/00207721.2026.2672127},
journal = {International Journal of Systems Science},
title = {Coupled policy algebraic equations for open-loop Nash equilibrium strategies in linear-quadratic games},
url = {http://dx.doi.org/10.1080/00207721.2026.2672127},
year = {2026}
}
TY - JOUR
AB - The characterisation and computation of open-loop Nash equilibrium strategies that admit a feedback synthesis for all initial conditions are revisited. First, it is shown that, provided certain structural assumptions are verified, the standard coupled, asymmetric Algebraic Riccati Equations can be entirely circumvented by relying on alternative equivalent conditions that are based on certain observability properties of the underlying state/costate dynamics, naturally arising in this context. Such conditions are linear in the matrices that constitute the unknowns of the standard coupled, asymmetric Algebraic Riccati Equations, although polynomial in the entries of the feedback gain matrices. Then, it is further shown how even such linear dependence can be entirely removed, thus yielding a set of conditions involving the feedback gain matrices alone. These conditions are referred to as the coupled Policy Algebraic Equations. While the dimension of the coupled, asymmetric Algebraic Riccati Equations grows quadratically with respect to the dimension of the state, the size of the latter grows instead linearly with respect to the state dimension, hence resulting in significant reduction in the number of the involved equations and independent variables.
AU - Astolfi,A
AU - Sassano,M
DO - 10.1080/00207721.2026.2672127
PY - 2026///
SN - 0020-7721
TI - Coupled policy algebraic equations for open-loop Nash equilibrium strategies in linear-quadratic games
T2 - International Journal of Systems Science
UR - http://dx.doi.org/10.1080/00207721.2026.2672127
ER -