This study develops a modified control algorithm for two identical pendulums under a common control input, incorporating two-sided energy constraints on the second pendulum. A Lyapunov function with barrier terms ensures the second pendulum’s energy remains within a predefined safe interval. The derived control law guarantees Lyapunov stability and drives the first pendulum’s energy asymptotically to a target value. Theoretical analysis confirms constraint satisfaction, establishes conditions to avoid undesirable invariant sets, and shows all equilibria are unstable or saddle points. Extensive numerical simulations validate the controller’s performance and robustness across various initial conditions and parameter settings, consistently achieving the energy goal while respecting the constraints. The algorithm demonstrates applicability without requiring retuning for different scenarios.