  Data-enabled predictive control (DeePC) has garnered significant attention
for its ability to achieve safe, data-driven optimal control without relying on
explicit system models. Traditional DeePC methods use pre-collected
input/output (I/O) data to construct Hankel matrices for online predictive
control. However, in systems with evolving dynamics or insufficient
pre-collected data, incorporating real-time data into the DeePC framework
becomes crucial to enhance control performance. This paper proposes an online
DeePC framework for time-varying systems (i.e., systems with evolving
dynamics), enabling the algorithm to update the Hankel matrix online by adding
real-time informative signals. By exploiting the minimum non-zero singular
value of the Hankel matrix, the developed online DeePC selectively integrates
informative data and effectively captures evolving system dynamics.
Additionally, a numerical singular value decomposition technique is introduced
to reduce the computational complexity for updating a reduced-order Hankel
matrix. Simulation results on two cases, a linear time-varying system and the
vehicle anti-rollover control, demonstrate the effectiveness of the proposed
online reduced-order DeePC framework.
