Linear Quadratic Zero-Sum Two-Person Differential Games
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, nongeneric, type of conjugate point. An important application of LQDGs is the so-called H ∞ -optimal control, appearing in the theory of robust control.
- Başar T, Bernhard P (1995) H ∞-optimal control and related minimax design problems: a differential games approach, 2nd edn. Birkhäuser, BostonGoogle Scholar