ECE PhD Proposal Review: Tianyu Dai

PhD Proposal Review: Data-Driven Control and Estimation

Tianyu Dai

Location: Zoom Link

Abstract: During the last two decades, data-driven control (DDC) has attracted growing attention in the control community. Unlike model-based control (MBC) that 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 important 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.

The aim of this proposal is to summarize our contributions to the DDC field. We mainly discuss the following problem: given a single trajectory of noisy data and a few priors of the model structure, how to design a state feedback controller to stabilize the system with unknown dynamics and in addition, to meet some performance criteria. 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.

This proposal is organized as follows: to start with, we propose a DDC framework for switched linear systems relying on the Farkas’ lemma to search for a common polyhedral control Lyapunov function using the theory of moments. Then to reduce the computational burden, we provide another method called data-driven quadratic stabilization control for linear systems that is based on quadratic Lyapunov function. To deal with nonlinear system, we first design data-driven controllers for polynomial systems using the dual Lyapunov theorem. Then to handle general nonlinearities, we propose a method based on state-dependent representations. Finally, a data-driven estimator is proposed that gives the worst-case optimal estimation of the trajectory of a switched linear system.