This paper reconsiders existence of worst-case Nash equilibria in noncooperative multi-player differential games, this, within an open-loop information structure. We show that these equilibria can be obtained by determining the open-loop Nash equilibria of an associated differential game with an additional initial state constraint. For the special case of linear-quadratic differential games, we derive both necessary and sufﬁcient conditions for solvability of the ﬁnite planning horizon problem. In particular, we demonstrate that, unlike in the standard linear-quadratic differential game setting, uniqueness of equilibria may fail to hold. A both necessary and sufﬁcient condition under which there is a unique equilibrium is provided. A sufﬁcient existence condition for a unique equilibrium is derived in terms of a Riccati differential equation. Consequences for control policies are demonstrated in a simple debt stabilization game.
|Journal||Optimal Control Applications & Methods|
|Early online date||17 Nov 2016|
|Publication status||Published - Sept 2017|
- robust control
- noncooperative differential games
- linear optimal control
- Riccati equations