Adaptive Neural Networks Based Optimal Control for Stabilizing Nonlinear System

The cart pole system (CPS) is a topic that has captured the interest of many academics, particularly control engineers, due to its nonlinear and underactuated characteristics. This paper proposes a control law to stabilize the system, using an optimal and intelligent controller such as LQRWFPI (Linear Quadratic Regulator with feedforward PI Controller) and supervised control with neural networks. A hybrid controller is introduced, combining the strengths of a neural controller improved with a LQRWFPI controller into a single system. An adaptive neuro-controller is trained offline to simulate the LQRWFPI controller, and then placed into the feedback loop where it continues to update its weights. The study achieves online adaptive control of a non-linear CPS using a Generalized Adaptive Linear Element (GADALINE), with the regularized LM algorithm utilized to train the linking weights of the neural controller offline, and the LSM algorithm used to train the ADALINE ANN online. The objective is to develop a quick and reliable neural network-based nonlinear controller for the CPS that can effectively handle disturbances, uncertainties, and nonlinearities that would cause other robust controllers to fail. Results demonstrate that the neural network controller can learn in real-time to mitigate disturbances and continue to operate the plant efficiently.