An approximate equivalence neural network to conventional neural network for the worst-case identification and control of nonlinear system

In this paper, we propose an approximate equivalence neural network model with a fast learning speed as well as a good function approximation capability, and a new objective function, which satisfies the H^∞ induced norm to solve the worst-case identification and control of nonlinear problems. The approximate equivalence neural network not only has the same capability of universal approximator, but also has a faster learning speed than the conventional feedforward/recurrent neural networks. Based on this approximate transformable technique, the relationship between the single-layered neural network and multilayered perceptrons neural network is derived. It is shown that a approximate equivalence neural network can be represented as a functional link network that is based on Chebyshev polynomials. We also derive a new learning algorithm such that the infinity norm of the transfer function from the input to the output is under a prescribed level. It turns out that the approximate equivalence neural network can be extended to do the worst-case problem, in the identification and control of nonlinear problems