Advances in Robust Control; and in High Resolution Spectral Estimation

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The research proposed herein represents a continuation of our current program in developing theoretical and computational tools for modeling and control of dynamical systems. Our plan is to investigate two main topics. 1. Robust control of nonlinear systems.Our approach relies on the concept of the graph. Model uncertainty is quantified using a suitable generalization of the gap metric which measures potential graph perturbations. A theory of robust control with explicit expressions for robustness margin is in place. Also, a computational approach has been presented in our recent work. The proposed research focuses on how to (i) enhance the effectiveness of the computational tools as well as seek more effective ones, (ii) extend the basic robustness theory outside the basic paradigm of stability about an equilibrium or a prespecified trajectory. In particular, we want to assess robustness of oscillatory systems, and systems in the presence of uncertain biases.2. High-resolution spectral estimation.The impetus for this direction was provided by recent joint work with Chris Byrnes and Anders Linquist. We have introduced filter banks, and subsequently general input-to-state (IS) filters, for providing harmonic amplification of selected spectral intervals. We are in the process of completing a general theory which takes advantage of the selectivity properties of such filters and allows very high resolution spectral estimation. In particular, for identifying sinusoids in noise, which is a key problem in radar and sonar applications, our approach has already permitted significantly better resolution than standard state-of-the-art MUSIC and ESPRIT algorithms.