Online Reduced-Order Data-Enabled Predictive Control

Data-enabled predictive control (DeePC) has garnered significant attention for its ability to achieve safe, data-driven optimal control without relying on explicit parametric models. Traditional DeePC methods use pre-collected input/output (I/O) data to construct a Hankel matrix offline and then formulate a predictive control framework online for linear, weakly nonlinear, and weakly stochastic systems. However, in systems with evolving dynamics, incorporating real-time data into the DeePC framework becomes crucial to enhance control performance. This paper proposes an online DeePC framework designed for strongly nonlinear and/or 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 three cases, linear time-varying system, vehicle anti-rollover control, and Li-ion battery fast charging, demonstrate the effectiveness of the proposed online reduced-order DeePC framework.