Reducing Conservatism in Robust Data-Driven MPC via the S-Variable Method and Time-varying Lyapunov Functions

Predictive control relies on a system model to forecast future behavior. In scenarios where a nominal model is unavailable, data-driven model predictive control techniques can compute control inputs directly from past measured trajectories. When the system is subject to noise and disturbances, the collected data becomes corrupted, potentially degrading control performance. By integrating robust control techniques with data-driven MPC, it is possible to ensure stability and robust constraint satisfaction in the presence of such uncertainty. Recent methods based on Linear Matrix Inequalities (LMIs) have shown promise in this direction, but often lead to conservative solutions due to structural limitations in the formulation. In this work, we propose a less conservative data-driven MPC scheme by incorporating a sequence of time-varying Lyapunov functions together with the S-variable approach. This enables a relaxation of the LMI conditions, decouples the controller design from the Lyapunov matrix, and improves feasibility and performance. We show that the resulting controller guarantees asymptotic stability and robust constraint satisfaction of the closed-loop system. A numerical example illustrates the effectiveness of the proposed approach compared to existing methods.