Abstract
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.
Original language | English |
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Pages (from-to) | 795-813 |
Journal | Optimal Control Applications & Methods |
Volume | 38 |
Issue number | 5 |
Early online date | 17 Nov 2016 |
DOIs | |
Publication status | Published - Sept 2017 |
Keywords
- robust control
- noncooperative differential games
- linear optimal control
- Riccati equations