On-line control of a nonlinear system using radial basis function neural networks

A control architecture that incorporates a radial basis function (RBF) neural network is proposed for the control of a particular nonlinear system, in this case the continuously stirred tank reactor (CSTR). The RBF network consists of Gaussian activation functions and is trained online to learn the inverse dynamics of the CSTR plant with and without parameter variation. Using Lyapunov stability theory, it is shown that the control architecture is globally stable for a sector-bounded nonlinearity in the error dynamics. Thus, the control architecture is capable of reducing the tracking error to a small region about zero. The size of this region is dependent on the approximation capabilities of the RBF network. Also, various input signals are investigated for their applicability to on-line function approximation. The simulation results validate the analytical results for stability and convergence in tracking error for a network with a set of fixed basis functions and suggest that stability and reduction in tracking error can be extended to a network with variable basis functions. In addition, the simulation results indicate that neural network consisting of local activation functions can approximate a function on-line provided the input signal sufficiently and frequently covers the input space of interest.