STABILITY AND OPTIMIZATION ANALYSES OF THE GENERALIZED BRAIN-STATE-IN-A-BOX NEURAL-NETWORK MODEL

Anderson's brain-state-in-a-box (BSB) neural network model may be viewed as a version of Hopfield's two-state neural model with continuous rather than discrete states and synchronous updating. A generalization of the BSB model which allows each model neuron in the system to have a bias and its own maximum and minimum firing rate is considered. Moreover, the generalization does not require that the matrix of connection weights be symmetric. A method of choosing the step constant of the algorithm is then described which guarantees that the generalized discrete-time BSB model: (i) approaches the largest set of system equilibrium points, and (ii) minimizes the Boltzmann machine quadratic energy function. A simple test (essentially a vector by matrix multiplication) for checking for asymptotically stable equilibrium points is also provided. Finally, a special case of the generalized BSB model is shown to be applicable to a particular type of optimal control problem. © 1993 Academic Press. All rights reserved.