Risk-Averse Designs: From Exponential Cost to Stochastic Games
We discuss the relationship between risk-averse designs based on exponential cost functions and a class of stochastic games, which yields a robustness interpretation for risk-averse decision rules through a stochastic dissipation inequality. In particular, we prove the equivalence between risk-averse linear filter designs and saddle-point solutions of a particular stochastic differential game with asymmetric information for the players. A byproduct of this study is that risk-averse filters for linear signal-measurement models are robust (through a stochastic dissipation inequality) to unmodeled perturbations in both the signal and the measurement processes.
KeywordsAttenuation Covariance Acoustics Estima
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- T. Başar and P. Bernhard, H ∞ -Optimal Control and Related Minimax Design Problems: A Dynamic Game Approach, Birkhäuser, Boston, MA, 2nd edition, 1995.Google Scholar
- W. H. Fleming and W. M. McEneaney, Risk Sensitive and Robust Nonlinear Filtering, Proceedings of the 36th IEEE CDC, San Diego, CA, 1997.Google Scholar
- S. K. Mitter, “Filtering and stochastic control: A historical perspective,” IEEE Control Systems Magazine, pp. 67–76, June 1996.Google Scholar
- P. Whittle. Risk-Sensitive Optimal Control, John Wiley and Sons, Chichester, England, 1990.Google Scholar