In this section
@article{Sassano:2025:10.1016/j.automatica.2024.111953,
author = {Sassano, M and Mylvaganam, T and Astolfi, A},
doi = {10.1016/j.automatica.2024.111953},
journal = {Automatica},
title = {OL-NE for LQ differential games: a Port-Controlled Hamiltonian system perspective and some computational strategies},
url = {http://dx.doi.org/10.1016/j.automatica.2024.111953},
volume = {171},
year = {2025}
}
TY - JOUR
AB - Linear Quadratic differential games and their Open-Loop Nash Equilibrium (OL-NE) strategies are studied with a threefoldobjective. First, it is shown that the state/costate lifted system (arising from the application of Pontryagin’s Minimum Principle)is such that its behavior restricted to the equilibrium subspace can be interpreted as the (non-power-preserving) interconnectionof two cyclo-passive Port-Controlled Hamiltonian systems. Such PCH systems constitute the best response generators for eachplayer, thus mimicking and extending the corresponding interpretation of (single-player) optimal control problems. Second, byrealizing that the behavior of the lifted dynamics off the equilibrium subspace is “irrelevant” for generating the equilibriumstrategies, it is shown that such an invariant subspace can be rendered, via a suitably constructed virtual input, externallyasymptotically stable while preserving the OL-NE. Finally, based on these premises we provide a closed-form gradient-descentmethod to solve the asymmetric coupled Riccati equations characterising the OL-NE strategies.
AU - Sassano,M
AU - Mylvaganam,T
AU - Astolfi,A
DO - 10.1016/j.automatica.2024.111953
PY - 2025///
SN - 0005-1098
TI - OL-NE for LQ differential games: a Port-Controlled Hamiltonian system perspective and some computational strategies
T2 - Automatica
UR - http://dx.doi.org/10.1016/j.automatica.2024.111953
UR - https://www.sciencedirect.com/science/article/pii/S0005109824004473
VL - 171
ER -