A switched reluctance motor (SRM) circuit drive system caused many nonlinear effects due to convex construction. The linear control methods were hard to achieve good performance for the SRM circuit drive. The adaptive nonlinear backstepping control system using switching function is proposed for controlling the SRM drive system to obtain good performance. To reduce chattering of control effort, the adaptive nonlinear backstepping control system using adaptive law is proposed to estimate the required lumped uncertainty. When the inertia of the counterweight is varying, this proposed method cannot get a satisfactory performance. The adaptive nonlinear backstepping control system using mended recurrent Romanovski polynomials neural network with adaptive law and error-estimated law is proposed for controlling the SRM drive system to raise robustness of the SRM drive system. Furthermore, two variable learning rates in the mended recurrent Romanovski polynomials neural network are adopted by using mended particle swarm optimization (PSO) algorithm to speed up parameter's convergence. Finally, comparative performances through some experimental results are verified that the proposed control system has better control performances than those of the proposed methods for the SRM drive system. KEYWORDS adaptive backstepping control, particle swarm optimization, recurrent Romanovski polynomials neural network, switched reluctance motor