Dynamic multilayer neural networks for nonlinear system on-line identification

To identify on-line a quite general class of nonlinear systems, this paper proposes a new stable learning law of the Dynamic Multilayer Neural Networks (DMNN). A Lyapunov-like analysis is used to derive this stable learning procedure for the hidden layer as well as for the output layer. An algebraic Riccati equation is considered to construct a bound for the identification error. The suggested learning algorithm is similar to the well-known backpropagation rule of the static multilayer perceptrons but with an additional term which assure the property of global asymptotic stability for the identification error. Two numerical examples illustrate the effectiveness of the suggested new learning laws.