Ergodic type Bellman equations of risk‐sensitive control with large parameters and their singular limits

Abstract

We consider existence of solutions of ergodic type Bellman equations of risk‐sensitive control with large parameters. Then we deduce as the singular limits first‐order nonlinear partial differential equations, which are considered to relate to $H_{\infty}$ control. This is a generalization of our previous work that appeared in Asymptotic Analysis 16 (1998), 347–362.