<p>Voltage Source Converter-based High Voltage Direct Current (VSC-HVDC) systems, particularly in the context of interconnecting asynchronous grids, face significant challenges related to system stability and dynamic response. These systems frequently utilize traditional controllers, such as Proportional-Integral (PI) regulators, which may prove inadequate in managing the nonlinearities and uncertainties intrinsic to VSC-HVDC systems, especially during disturbances. This paper presents an Adaptive Backstepping Control (ABC) methodology, optimized through Particle Swarm Optimization (PSO), tailored for an asynchronous VSC-HVDC system. The Adaptive Backstepping approach, grounded in Lyapunov stability theory, facilitates robust control over system nonlinearities and varying parameters; however, the process of determining optimal control gains can be labor-intensive and reliant on trial-and-error methods. To mitigate this challenge, PSO is employed to systematically optimize these parameters, thereby enhancing the stability and performance of the system. The proposed controller effectively regulates DC voltage, active and reactive power, while smoothly adapting to changing system conditions. Its robustness is evaluated under disturbances. Simulation results indicate that the integration of Adaptive Backstepping and PSO significantly improves system response and eliminates steady-state error. This advanced control scheme exemplifies the potential of combining Adaptive Backstepping with optimization techniques, establishing it as a viable solution for intricate power system applications.</p>