Learning state space trajectories in cellular neural networks

A learning algorithm similar to the backpropagation-through-time approach is presented. The algorithm is based on the minimization of an error criterion, which is defined as the product of a function of the state at a given time and the integral of an entire time function of the state over the trajectory prior to this time. The technique of the calculus-of-variation is used to evaluate the gradient of the error in the parameter space, which can be used to descend to a minimum on the error surface. This theory is adapted to cellular network networks (CNNs) and some simple examples of the learning of CNN parameters are shown