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

Article type: Research Article

Authors: Kaise, Hidehiro | Nagai, Hideo^{; ;}

Affiliations: Department of Mathematical Science, Graduate School of Engineering Science, Osaka University, Toyonaka, 560‐8531, Japan E‐mail: {kaise, nagai}@sigmath.es.osaka‐u.ac.jp

Note: [] Corresponding author.

Note: [] Research supported in part by Grant‐in‐Aid for Scientific Research No. 10440030, the Ministry of Education, Science and Culture, Japan.

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.

Journal: Asymptotic Analysis, vol. 20, no. 3‐4, pp. 279-299, 1999