Risk-Coherent $\mathcal{H}_{\infty}$ -optimal Filter Design Under Model Uncertainty with Applications to MISO Control

This work presents a framework to address the problem of designing discrete-time LTI (linear and time-invariant) multiple-input and multiple-output (MIMO) filters, aiming to optimize the performance of a system when model uncertainty is considered. Additionally, we present an interesting application to control design for disturbance rejection under model uncertainty. To account for this uncertainty we employ coherent measures of risk, which are a family of measures in theory of risk. We particularly discuss which measures are suitable by comparing the conditional value-at-risk (CVaR) to other three common designs. Using a scenario approach, we derive a convex optimization problem based on linear matrix inequalities (LMIs), whose solution minimizes the risk of falling into poor $\mathcal{H}_{\infty}$ performance. Finally, we present an application to multiple-input and single-output (MISO) control design under model uncertainty in the auto-covariance function of the output noise, comparing approaches minimizing different notions of risk.