Analytical study of a control algorithm based on emotional processing

Abstract

This work presents a control algorithm developed from the mammalian emotional processing network. Emotions are processed by the limbic system in the mammalian brain. This system consists of several components that carry out different tasks. The system level understanding of the limbic system has been previously captured in a discrete event computational model. This computational model was modified suitably to be used as a feedback mechanism to regulate the output of a continuous-time first order plant. An extension to a class of nonlinear plants is also discussed. The combined system of the modified model and the linear plant are represented as a set of bilinear differential equations valid in a half space of the 3-dimensional real space. The bounding plane of this half space is the zero level of the square of the plant output. This system of equations possesses a continuous set of equilibrium points which lies on the bounding plane of the half space. The occurrence of a connected equilibrium set is uncommon in control engineering, and to prove stability for such cases one needs an extended Lyapunov-like theorem, namely LaSalle's Invariance Principle. In the process of using this Principle, it is shown that this set of equations possesses a first integral as well. A first integral is identified using the compatibility method, and this first integral is utilized to prove asymptotic stability for a region of the connect equilibrium set.