Robust universal neural controllers

Here we introduce the class of neural controllers called integrable basis function neural controllers (IBFNC) consisting of a fixed neural network architecture employing a fixed integrable basis function in the nodes of the single hidden layer. Our main result shows the existence of arbitrarily precise IBFNC approximations of a class of robustly stabilizing controllers for a certain large and important class of nonlinear uncertain plants. It should be emphasized that a fixed IBFNC architecture (defined by the width and the centers of the basis function) is used to obtain a controller for any plant belonging to the given class, with the same error bound. The only parameters that need to be recomputed for the new plant are the weights from the hidden nodes to the output. But this computational problem is linear. These results show that IBFNCs are powerful and efficient for robust control, being linearly reconfigurable neural controllers that are universal for the class of plants under consideration. An interesting practical implication bearing on the problem of parameter determination of the IBFNC is the following. Concerning the usual practice of splitting the parameter determination problem into a nonlinear part of determining the width and the centers and the linear part of estimating the output weights. The results obtained here show that the computationally expensive nonlinear part needs to be solved only once for a given class of equicontinuous controllers. The remaining part arising due to a change in the controller is computationally easy, being linear.