Effective feedback control is essential for optimizing dynamical systems by minimizing a predefined cost function, thereby stabilizing the system toward a desired state. Despite its proven effectiveness, the applicability of feedback control is often limited by the high dimensionality of state spaces, especially in parametric settings. To address these challenges, we apply Riccati-based Dynamical Low-Rank Approximation (R-DLRA). In practice, the standard DLRA basis is enriched with information related to the solution of the State-Dependent Riccati Equations (SDREs), yielding efficient, accurate solutions for high-dimensional feedback control problems. To solve the SDRE solutions, we propose a Cascade Newton-Kleinman (C-NK) algorithm, which leverages prior parametric and time knowledge of the Riccati solution, to improve the convergence of Newton-based methods applied to SDREs across different parameters and time instances. Our approach significantly accelerates the solution process for infinite horizon optimal control by constructing a low-dimensional, compact representation of the evolving system, thereby enhancing both accuracy and real-time control across multiple parametric instances. The proposed R-DLRA approach demonstrates faster and more accurate performance than the full-order model, when compared to the standard DLRA, global Proper Orthogonal Decomposition (POD), and Riccati-based POD.