This article describes the use of an enhanced sliding surface and a Quasi-Newton algorithm for mobile robot control. To enhance performance and reduce chattering around a sliding surface, a proportional-integral sliding surface (PI-SS) is used. The objective of the proportional-integral sliding mode control declared in this study is to provide a switching control law that will allow the system’s output to get closer to the references and significantly lessen chattering. Regarded as the most well-liked and effective method for resolving unconstrained optimization issues is the Quasi Newton algorithm. The radial basis function neural network (RBF-NN), which approximates the nonlinear elements in the sliding mode controller, is trained using this approach. According to this proposed controller, the confirmed trajectory of the mobile robot will converge to the request trajectory in finite time. By using Lyapunov’s theory, the system’s stability is demonstrated. The efficacy of the suggested controller is demonstrated by the MATLAB/Simulink simulation results, which show that the chattering phenomenon was reduced and that the steady-state error converged to zero, the rising time reached 0.2284 s, the settling time was 0.4454 s, the overshoot was 1.9984e-13 % in x-coordinate; 0.2285 s, 0.4456 s, 1.5543e-13 % in y-coordinate, respectively.