From the introduction: A modular Recurrent Dynamic Neural Network (RDNN) that has been used in previous research to solve uncertain linear and nonlinear signal representation problems is applied to the optimal control problem of a simulated nonlinear Slider Inverted Pendulum (SIP). The advantage of using neural networks is their robustness when dealing with uncertain and ill-conditioned problems. Effectively, when compared with LU decomposition in solving linear systems corrupted with noise, the RDNN solution is less sensitive to noise. Optimal control of the SIP is carried out using the analytical Linear Quadratic Regulator (LQR) technique, where the control gains are derived from the solution of the Algebraic Riccati Equation (ARE) by computing the eigenvalues and eigenvectors of the Hamiltonian matrix $H$. In the case of noise in the control loop of the SIP, caused possibly by external disturbances or sensitive sensors, $H$ becomes noise corrupted. This could lead to inaccurate LQR control gains when solving the problem with standard numerical methods. By transforming the problem into a set of linear systems of equations, and combining the RDNN with a steepest descent method, we propose a neural-based method to compute the LQR control gains, and we show the robustness of this method in the presence of noise. Furthermore, the stability of the overall LQR/RDNN neural controller is demonstrated. We then apply this neural control method to the SIP by designing two controllers about two different operating points. The performance of both neural controllers is successful in the vicinity regions of their respective operating points. The satisfactory results obtained show that the RDNN represents a fitting and useful tool in the robust optimal neural control of a SIP.