To address the problems that the SPGD algorithm suffers from a significant decrease in convergence speed and a high risk of being trapped in local optima as the number of coherently combined beams increases and atmospheric turbulence intensifies, a staged parameter-adaptive SPGD algorithm is proposed.

The algorithm divided the optimization process into an early convergence stage and a late convergence stage based on the value of the objective function. In the early stage, a cosine decay function with a faster attenuation rate was employed to adaptively adjust the gain coefficient and perturbation voltage, thereby enhancing the global search capability, accelerating convergence to the optimal solution, and reducing the likelihood of being trapped in local optima. In the late stage, an exponential decay function with a slower attenuation rate was adopted to refine the adjustment of the gain coefficient and perturbation voltage, which mitigated oscillations around the optimal solution and improved convergence accuracy.

In the proposed algorithm, the early stage used the cosine decay function to rapidly adjust the gain coefficient and perturbation voltage, while the later stage used the exponential decay function to achieve smoother and finer adjustment. Using this algorithm as the phase control strategy, coherent combining simulations for 3, 7, and 19 beams were conducted, respectively. The results indicated that, compared with the traditional SPGD algorithm, the convergence speed improved by 16.7%, 27.7%, and 37.4% (Fig.13).

The staged parameter-adaptive SPGD algorithm adaptively adjusts the gain coefficient and perturbation voltage at different stages by introducing cosine and exponential functions, effectively verifying the feasibility of staged parameter-adaptive adjustment and its application value in multi-beam laser coherent combining systems.