Design of Globally Robust Control for Biologically- Inspired Noisy Recurrent Neural Networks

Recurrent neural networks have become one of the most promising methodologies to solve various difficult problems in different scientific areas, such as system identification and control, pattern recognition, image processing, modeling biological sensor-motor systems, etc. Therefore, theoretical studies on both stability and controllability of recurrent neural networks have received much attention during the last several years, see for example, (Arik, 2000; Ensari & Arik, 2005; Hu & Wang, 2002; Kulawski & Brdys, 2000; Liu, Torres, Patel, & Wang, 2008; Marco, Forti, & Tesi, 2004; Sanchez & Perez, 2003; Sontag & Qiao, 1999; Sontag, 1989), and references therein. However, these studies primarily focused on these mathematical models, which do not consider the noise process that is fraught with signal transmission particularly in biological systems. On the other hand, Haykin (Haykin, 1999) indicated that the synaptic transmission is a noise ABSTRACT