@article{27f722836de940ae8dbbb7d6e3bf1dbe,
title = "Riccati Equations in Nash and Stackelberg Differential and Dynamic Games",
abstract = "The purpose of this paper is to provide an overview of various types of Riccati differential and difference equations (RDEs) and the associated algebraic Riccati equations (AREs) that arise in various classes of linear quadratic (LQ) differential and dynamic games. We first study generalized RDEs and AREs in LQ zero-sum differential games, and then consider coupled RDEs and AREs in LQ nonzero-sum differential games. We also discuss some nonsymmetric RDEs in LQ Stackelberg differential games, and RDEs in LQ dynamic games.",
keywords = "Riccati differential, algebraic Riccati equations, difference equations, linear quadratic differential games",
author = "Tamer Ba{\c s}ar and Jun Moon",
note = "Funding Information: ★This research was supported in part by the Office ofi Naval ReTsehairschre(sOeaNrcRh) wMaUs RsIupgpraonrtedN0i0n01p4a-r1t6-1b-y27t1h0e, iOnffpicaertobfiyNNavSaFl ReThissearchre(ONsearcRh)wMaUsRsuppIgraortedntN00014-16-1-2710,in part by theinOfficepartofibyNNavSFal unedseearrgcrhan(tOCNCRF)1M1-U11R3I42g,raanndt iNn0p0a0r1t4b-y16t-h1e-2B7a1s0ic, SinciepnacretRbeyseNarScFh Research (ONR) MURI grant N00014-16-1-2710, in part by NSF PnrodgerragmratnhtrCouCgFh1t1h-e1N13a4t2io,naanldRinespeaarrtchbyFothuendBaatsiiocnSocfiieKnocreeRaefisuenadrecdh Program through the National Research Foundation ofi Korea fiunded Program through the National Research Foundation ofi Korea fiunded by the Ministry ofi Science, ICT, and Future Planning under Grant by the Ministry ofi Science, ICT, and Future Planning under Grant 2016R1C1B1015474. 2016R1C1B1015474. Publisher Copyright: {\textcopyright} 2017",
year = "2017",
month = jul,
doi = "10.1016/j.ifacol.2017.08.1625",
language = "English (US)",
volume = "50",
pages = "9547--9554",
journal = "IFAC-PapersOnLine",
issn = "2405-8963",
publisher = "IFAC Secretariat",
number = "1",
}