Robust optimal control using recurrent dynamic neural network

A modular recurrent dynamic neural network (RDNN) based on the Hopfield model is applied to the linear quadratic regulator (LQR) optimal control of a nonlinear slider inverted pendulum (SIP). The main advantage of using neural networks is their robustness and flexibility when dealing with uncertain and ill-conditioned problems. The combination of the RDNN with LQR control is done in two ways. In the first technique, the LQR control gains are calculated by solving the algebraic Riccati equation (ARE) using the RDNN. Robustness of the control is further improved by appropriately tuning the LQR gains. In the second technique, the RDNN is trained to learn the connections between the controller's inputs and outputs. The efficacy of the training is confirmed as the neural controller performs successfully when tested on-line. Neural control results in more robustness, especially when noise is added to the system. The overall positive results of this study show that the proposed LQR/RDNN control offers an efficient alternative to traditional LQR control when dealing with noise corrupted data, and confirm the feasibility of using neural networks in the design of robust optimal controllers.