The Chebyshev polynomials based unified model (CPBUM) neural network for the identification and control of nonlinear H∞ problems

In this paper, the authors propose a 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 identification and control of nonlinear H_∞ problems. Based on this approximate transformable technique, the relationship between the single-layered neural network and multi-layered perceptrons neural network is derived. It is shown that the Chebyshev polynomials-based unified model neural network can be represented as a functional link network that is based on Chebyshev polynomials. They 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 Chebyshev polynomials-based unified model neural network can be extended to the worst-case problem, in the identification and control of nonlinear H_∞ problems.