Fourier ptychographic microscopy (FPM) is recently proposed as a computational imaging method to bypass the limitation of the space-bandwidth product of the traditional optical system. It employs a sequence of low-resolution images captured under angularly varying illumination and applies the phase retrieval algorithm to iteratively reconstruct a wide-field, high-resolution image. In current FPM imaging system, system uncertainties, such as the pupil aberration of the employed optics, may significantly degrade the quality of the reconstruction. In this paper, we develop and test a nonlinear optimization algorithm to improve the robustness of the FPM imaging system by simultaneously considering the reconstruction and the system imperfections. Analytical expressions for the gradient of a squared-error metric with respect to the object and illumination allow joint optimization of the object and system parameters. The algorithm achieves superior reconstructions when the system parameters are inaccurately known or in the presence of noise and corrects the pupil aberrations simultaneously. Experiments on both synthetic and real captured data validate the effectiveness of the proposed method.