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This research is concerned with the design of radial basis function neural networks to implement a controller for nonlinear systems. Nonlinear systems are of particular interest given the fact that most real life systems are nonlinear in nature and control schemes for such systems are not as developed as their linear counterparts and involves a lot of heuristics. We show the ability of radial basis function networks (RBF) to serve as a single unifying model incorporating both nonlinear and linear methodologies. We focus on the problem of the inverted pendulum on a cart system, which is a classic problem in a lot of control literatures. The problem is to swing the pendulum from a given initial state, which is typically the hanging down position, to the up position and then to keep it balanced in the up position. In swinging the pendulum, the cart to which the pendulum is attached is moved back and forth on a track until the pendulum is in the up position. This system is a very useful model in that it demonstrates a multi-variable highly nonlinear system that belongs to a class of nonlinear systems that cannot be controlled by traditional nonlinear techniques such as feedback linearization. In training the RBF network, we explore several different control schemes to produce the training data. These control schemes could also be easily extrapolated to work with other multi-variable nonlinear systems. We first design a neural controller for the second order system describing the pendulum dynamics only. The controller is able to drive the state variables from any permissible state of the system to zero, and to keep it stabilized in that equilibrium state. Secondly, we again show the network's ability to implement nonlinear control of the fourth order pendulum/ cart system. We

Neural Network Implementation of Non Linear Control Using Radial Basis Functions