Risk sensitive optimal control and differential games. (English) Zbl 0788.90097
Duncan, T. E. (ed.) et al., Stochastic theory and adaptive control. Proceedings of a workshop held at Lawrence, KS (USA), September 26-28, 1991. Berlin: Springer-Verlag. Lect. Notes Control Inf. Sci. 184, 185-197 (1992).
Summary: Risk-sensitive stochastic control problems for nonlinear systems described by stochastic differential equations are considered. A logarithmic transformation is applied to the optimal cost function. The value function for a zero-sum, two-controller differential game is obtained in the limit, as a small parameter which represents noise intensity tends to zero. Convergence to the value function is proved by viscosity solution methods for nonlinear partial differential equations.
For the entire collection see [Zbl 0778.00021].
For the entire collection see [Zbl 0778.00021].
MSC:
| 91A23 | Differential games (aspects of game theory) |
| 49L25 | Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games |
| 93E20 | Optimal stochastic control |
| 49J20 | Existence theories for optimal control problems involving partial differential equations |
