Connectionist Approach to Non-linear Internal Model Control Using Gaussian Approximation

In this work we focus on the use of adaptive connectionist networks for identification and control of non-linear dynamic systems. The ability of connectionist models to represent arbitrary non-linear relations is by now well established [1]. This has lead to the investigation of non-linear dynamic systems modelling using connectionist representations [2]. Of particular importance in the control context is the modelling of inverse dynamical relationships. A feature of our approach is the use of radial basis functions, and the Gaussian function in particular, as the non-linear function in the network hidden units [3]. There is recent theoretical support for the `best representation´ property of such networks [1]. This approach stands in contrast to the widespread use of sigmoidal non-linearities. Gaussian networks were recently studied in the context of dynamical systems identification by Chen et al [4]; this type of network has also been studied in the related problem of time series prediction [5]. Finally, we propose the use of connectionist models of plants and their inverses as elements in an Internal Model Control feedback structure.