<p>This paper presents a mathematical model of a two-degree-of-freedom (2-DOF) electrostatically coupled double-beam resonator and conducts a comprehensive analysis of its complex nonlinear dynamic behavior. Owing to the interplay between electrostatic coupling and nonlinear restoring forces, the system exhibits a rich spectrum of dynamic behaviors, including periodic, quasi-periodic, and chaotic oscillations. To analyze the onset and evolution of chaotic motion, the potential energy function is employed to identify regions of instability. The presence of chaos is further confirmed through bifurcation diagrams and phase portraits. In order to address the challenge of chaotic oscillations and improve system stability, an intelligent control strategy based on the Independent Deep Q-Network (IDQN) is proposed. In this framework, multiple agents are trained independently to collaboratively regulate the system's response, effectively suppressing chaotic behavior. Once trained, the agents are implemented on an STM32 microcontroller, forming an IDQN-based control network capable of real-time regulation of the resonator. Subsequently, a kinematic model of the Simulated 2-DOF electrostatically coupled double-beam resonator is deployed on a DSP platform and integrated with the IDQN control network to realize real-time chaos suppression. Experimental results confirm that the proposed IDQN-based control method successfully mitigates chaotic oscillations, with the observed system dynamics closely aligning with numerical simulation results.</p>