Tianyu Dai’s PhD Dissertation Defense

“Robust Data-Driven Control”

Abstract:

During the last two decades, data-driven control (DDC) has attracted growing attention in the control community. Unlike model-based control (MBC), which first uses the collected data to identify the system, then designs the controller according to the certainty equivalence principle, DDC skips the system identification (SYSID) step and leads to a control law directly from data. One crucial feature of DDC is that some fundamental limitations of MBC, such as uncertainty versus robustness, inevitable modeling error, and possible expensive cost of SYSID, are avoided in the DDC framework. These benefits enable the researcher to design controllers with better performance and accuracy.

Robust data-driven control (RDDC) as a branch of DDC has developed rapidly in recent years, focusing on the data-driven controller design for the state space model. It aims to solve the following problem: given a single trajectory of noisy data and a few priors of the model structure, how to design a robust state feedback controller to stabilize the system with unknown dynamics, and in addition, to meet some performance criteria. By robust, we mean the learned controller can stabilize all possible systems residing in the set compatible with the noisy data.

This dissertation aims to summarize our contributions to the RDDC field. We focus on the L_infinity bounded noise, and the main idea hinges on duality theory to establish the connection between two sets, one compatible with the noisy data and the second satisfying some design properties such as stability or optimality. Our main results show that for all possible systems compatible with the data, the data-driven control law can be obtained by solving a convex optimization problem. In the dissertation, we propose RDDC algorithms for linear, switched, and nonlinear systems with process noise, extend results for error-in-variables (a more general case), and discuss a worst-case optimal estimation of the trajectory of a switched linear system.

Committee:

Prof. Mario Sznaier (Advisor)

Prof. Octavia Camps
Prof. Bahram Shafai

Prof. Eduardo Sontag