Nonlinear data-driven control
Learning controllers from data is of utmost importance and a fascinating topic, with foundations in both control theory and data science. With her thesis, Xiaoyan Dai contributes to analytically correct data-driven control methods with computationally efficient data-dependent LMIs whose feasible solutions provide controllers and performance certificates.
Firstly, Dai considers the output feedback control problem of poorly known systems from input-output data and some prior knowledge. She derives optimal output feedback control methods for unknown linear systems that bypass model identification or a separate design of a state observer and a state feedback controller.
Then, Dai develops data-driven output feedback control methods for a general class of nonlinear systems by enforcing a closed-loop system dominated by stable linear dynamics. To this end, she uses a growth condition on the basis functions and input-output data. Notably, Dai extends the methods to cope with the cases with input-output measurement noise and an incomplete dictionary of basis functions.
Finally, Dai considers the online control of input-affine nonlinear systems via time-varying SDPs. Both model-based and data-driven solutions are derived where control gains are correctly adapted. Dai derives compact conditions that certify recursive feasibility from data.