Verification on the approximate theorem of time-varying RBF neural networks and its application analysis

Aiming at the status that few effective methods is available on dealing with time-varying nonlinearities, we put forward the idea of introducing time-varying factors into the RBF NN structure, which using neural networks with time-varying weight to approximate time-varying nonlinearities. We prove the theorem that a time-varying nonlinear function defined on the finite time interval can be approximated by an at least piecewise continuous time-varying weight vector and a finite number of neuron basis functions with expected precision, which provides theoretical support for the usage of time-varying neural networks. Subsequently, the application mode of the time-varying NN is discussed, which introduce a new idea to solve the control problem of time-varying nonlinear systems.