State estimation of continuous time radial basis function networks

The problem of state estimation for continuous time dynamic RBF (radial basis function) networks using minimax approach is addressed. The uncertainty class is characterized in terms of an approximation error vector. Minimizing the objective function over this uncertainty class is used to obtain state estimates. The paper presents the derivation and properties of such a minimax state estimator for RBF networks. This is then extended to the problem of minimax adaptive state estimation. This approach is useful in the cases where the pretrained RBF network is to be used in state estimation, since the latest information is used in improving estimates of the RBF weights. A special class of estimators for the appended state estimation problem is also considered where a constant gain estimator matrix can be obtained. This section gives sufficient conditions for the existence of such an observer and follows directly from the structure of the RBF networks