Data-Driven Safe Exploration to Enhance Robust Performance

We propose a novel optimization-based safe exploration strategy for improving the robust performance of linear time-invariant systems. At each time step, the exploratory control input is obtained by solving a data-based semidefinite program (SDP) that ensures robust satisfaction of safety constraints and recursive feasibility for all admissible disturbances and all system dynamics consistent with the available data. Furthermore, the SDP is designed to systematically guide exploration toward trajectories that are most informative for reducing the worst-case performance bound. A simulation example demonstrates that the proposed performance-oriented exploration strategy achieves significantly improved robust performance compared to a safe maximum-energy exploration baseline.