ℒ₂ ℒ_∞ learning of dynamic neural networks

This paper proposes an ℒ₂ ℒ_∞ learning law as a new learning method for dynamic neural networks with external disturbance. Based on linear matrix inequality (LMI) formulation, the ℒ₂ ℒ_∞ learning law is presented to not only guarantee asymptotical stability of dynamic neural networks but also reduce the effect of external disturbance to an ℒ₂ ℒ_∞ induced norm constraint. It is shown that the design of the ℒ₂ ℒ_∞ learning law for such neural networks can be achieved by solving LMIs, which can be easily facilitated by using some standard numerical packages. A numerical example is presented to demonstrate the validity of the proposed learning law.