Integrated Learning Based Control Framework for Stabilizing Discrete-Time Dynamical Systems

This paper investigates the stabilization problem of discrete-time linear and nonlinear systems under uncertainties and external disturbances. A dynamic Lyapunov-based control framework is proposed to improve stability and convergence performance. The framework incorporates data-driven adaptation to address unknown or time-varying system dynamics and employs parallel computational structures to enable efficient real-time stability evaluation. The proposed method enhances robustness and convergence speed without imposing restrictive assumptions on system models. Numerical studies under stochastic perturbations, parameter variations, and boundary operating conditions demonstrate up to a 50% improvement in convergence speed and a 25% enhancement in stability prediction accuracy compared to conventional approaches. Further validation through large-scale simulations and hardware-in-the-loop experiments on aerospace benchmark systems confirms the effectiveness and practical applicability of the proposed framework.