Computer Science Department
School of Computer Science, Carnegie Mellon University


Differential Hybrid Games

André Platzer

December 2014


Also appears as: Differential hybrid games.
ACM Transactions on Computational Logic 18(3), 2017
DOI 10.1145/3091123

Keywords: Differential games, hybrid games, logic, differential game invariants, partial differential equations, viscosity solutions, real algebraic geometry

This paper introduces differential hybrid games, which combine differential games with hybrid games. In both kinds of games, two players interact with continuous dynamics. The difference is that hybrid games also provide all the features of hybrid systems and discrete games, but only deterministic differential equations. Differential games, instead, provide differential equations with input by both players, but not the luxury of hybrid games, such as mode switches and discrete or alternating interaction. This paper augments differential game logic with modalities for the combined dynamics of differential hybrid games. It shows how hybrid games subsume differential games and introduces differential game invariants and differential game variants for proving properties of differential games inductively.

44 pages

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