A conjugate Hopfield neural network for optimum systems control

A general neuromorphic procedure for solving a class of optimal control problems is presented. The method consists of transformation of the optimal control problem into a two-point boundary-value problem which then is converted to the problem of minimization of an error function over a field of scalars. This error function is then mapped into the energy function of the Hopfield-Tank neural network, leading to synaptic interconnection weights and input bias currents which are adapted to the problem to be solved. The author also develops the architecture of a modified Hopfield type network based on the conjugate gradient minimization of a function. This conjugate Hopfield network shows quadratic convergence performance compared to linear convergence of the usual Hopfield network. The method is illustrated by examples. Engineering realization of the network can be achieved via dedicated VLSI circuits. Alternatively, the method can be used for simulation on parallel computers