Linear Quadratic Zero-Sum Two-Person Differential Games

Pierre Bernhard (1)

1 BIOCORE - Biological control of artificial ecosystems

As in optimal control theory, linear quadratic (LQ) differential games (DG) can be solved, even in high dimension, via a Riccati equation. However, contrary to the control case, existence of the solution of the Riccati equation is not necessary for the existence of a closed-loop saddle point. One may " survive " a particular, non generic, type of conjugate point. An important application of LQDG's is the so-called H∞-optimal control, appearing in the theory of robust control.

Mots clés: H-infinity-optimal; Linear Quadratic; Riccati equation

Domaines: Automatique; Mathématiques [math]; Sciences de l'ingénieur [physics]

Pierre Bernhard. Linear Quadratic Zero-Sum Two-Person Differential Games. Encyclopaedia of Systems and Control, Springer-Verlag, pp.6, 2015, ⟨10.1007/978-1-4471-5102-9_29-1⟩. ⟨hal-01215550⟩