Data-Driven Positivity-Preserving Optimal State-Feedback Control via Successive Convex Programming

This letter introduces a successive convex programming approach to solve the data-driven optimal linear quadratic regulator (LQR) problem with positivity-preserving constraints. While positivity-preserving stabilization of linear time-invariant (LTI) systems is convex due to the existence of a linear copositive or diagonal Lyapunov matrix, this property does not apply to positivity preserving LQR performance. Adding positivity constraints disrupts the convexity of both model-based and data-driven optimal state-feedback designs. This letter is the first to address the data-driven LQR problem with positivity constraints. Assuming that the system dynamical model is unknown but the measurement data are available, this letter derives an equivalent formulation for the non-convex data-based problem and presents a successive convex optimization method using $\epsilon $ -perturbed semi-definite programs (SDPs) to monotonically decrease the cost and ensure convergence to a stationary point of the original problem. The method also supports structured controller design. Finally, its optimality, convergence, sensitivity to initialization, and comparison with the existing methods are analyzed through numerical case studies, demonstrating its effectiveness in data-driven control synthesis.