We address the problem of developing efficient optimization algorithms relevant to system identification and data-driven controller design. We devote particular attention to constrained optimization problems. In this context, we consider polynomial optimization [1] and propose a framework to develop algorithms based on feedback controller design [2]. Current developments in this direction include extending the framework in [2] to inequality constraints and applying the proposed algorithm to the training of recurrent neural networks.

We address the problem of estimating bounds on the parameters of continuous-time LTI systems, considering black-box and gray-box models. We cast the problem in the set membership framework and provide a solution based on polynomial optimization.
We also address the more general nonlinear system identification problem. We consider input-output models and propose a solution based on the optimization algorithms mentioned above.

We address the problem of directly designing feedback controllers from data without resorting to plant estimation/identification. We place particular emphasis on guaranteeing the feedback system's stability in the presence of finite data and bounded noise.