Adaptive learning control using affine radial basis function network approximation

A new paradigm for learning control of a generic nonlinear system is presented. The method is based on a special radial basis function network architecture and is adaptive as the input/output properties of the system are estimated and the learning control gain is computed online. The controlled system is described with a mapping between the feedforward control and an array of sampled output values over a given time interval. The network approximates the system input/output mapping as a function of the task parameter vector comprising the initial and a desired final system state. The approximation is affine and linear in the control input. For given network weights, this allows inverting the network approximation and an optimal control program. The network weights are updated depending on the results of the learning trials. The application of the algorithm to the control of an arbitrary planar motion of a two link arm demonstrates fast learning and the high accuracy of the method