Based on both the kinematic and the dynamic models of Wheeled Mobile Robots (WMRs), an optimal circumnavigation controller around moving targets is proposed by integrating backstepping control with adaptive dynamic programming (ADP) techniques. Initially, the cooperative circumnavigation challenge at the kinematic level is converted into a tracking task for the desired relative velocity by establishing a relative velocity error model between the robot and the target. Then, a dynamic-level error model is formulated to characterize the positional and directional errors between the robot's trajectory and the trajectory derived from the kinematic analysis. The control input is designed through the integration of the backstepping control and ADP. Ultimately, the proposed control strategy is proven to ensure both closed-loop system stability and the minimization of the cost function through Lyapunov’s method. Simulation comparisons with traditional methods confirm both the feasibility and superiority of the proposed controller.