Design Criteria for Estimation and Control with Bounded Data Uncertainties

There are always discrepancies between design models and the actual physical systems or phenomena that they model. These discrepancies can be due to several factors including the approximation of complex models by simpler ones, the presence of unavoidable experimental errors when collecting data, or even due to unknown or unmodeled effects. Regardless of their source, such perturbations can seriously degrade the performance of otherwise optimal designs. Examples to this effect abound in the fields of signal and image processing, digital communications, control, and others.

These possibilities have motivated over the years numerous investigations on design techniques that are less sensitive to such perturbations. In this talk, we provide an overview of recent research efforts in our group on novel design strategies for models and data with bounded perturbations. The new formulations are rich in geometry and rely on constrained game-type scenarios that even allow for smart adaptive opponents. The framework is broad enough to encompass applications across several disciplines, including both signal processing and control. Examples and comparisons will be given in the context of quadratic control design, image restoration and image separation, adaptive filtering, total-least-squares designs, and generalized cross-validation techniques.

Despite the results already obtained, several issues remain open and indicate potential future developments with interesting ramifications; these will be briefly discussed.