A Data-Enabled Primal-Dual Approach for Policy Learning with SDP Formulations
For control engineers, it provides an efficient online method to learn optimal policies from data while handling SDP constraints, though incremental over existing primal-dual and data-driven control approaches.
This paper proposes a data-enabled primal-dual framework for online policy learning in unknown linear systems, updating control policies via lightweight iterations instead of solving full SDPs. It achieves local linear tracking and global ergodic convergence, demonstrated on LQR, H∞ control, and safe exploration.
This paper develops a data-enabled primal-dual framework for learning optimal control policies for unknown linear discrete-time systems from online data. The proposed approach views the data-dependent control synthesis problem as a time-varying semidefinite program (SDP) whose coefficients are recursively updated from online closed-loop measurements. Instead of repeatedly solving a full SDP as new data arrive, the policy is updated online through lightweight primal-dual iterations, each consisting of a linear equation solve and a projection onto the positive semidefinite cone. The framework applies to both direct and indirect data-driven formulations and covers a broad class of control objectives, including LQR, $H_\infty$ control, and safety-critical control. To characterize the coupling between online optimization and closed-loop data generation, we introduce two data-dependent quantities: the Sim-to-Real Gap, which measures the mismatch between noisy and noiseless data-induced SDPs, and the Difference-of-Signal, which measures the temporal variation of the SDP coefficients. Under persistency of excitation, suitable SDP regularity conditions, and sufficiently slow data variation, we establish a local linear tracking result up to residual terms governed by the latter two quantities. A global ergodic convergence bound is also derived for arbitrary initialization. Numerical examples on LQR, $H_\infty$ control, and safe exploration demonstrate that the proposed method can efficiently improve control performance from online data while accommodating SDP constraints beyond the well-explored LQR policy-gradient formulations.