NEURAL NETWORKS FOR FEEDBACK FEEDFORWARD NONLINEAR CONTROL-SYSTEMS

This paper deals with the problem of designing feedback feedforward co ntrol strategies to drive the state of a dynamic system (in general, n onlinear) so as to track any desired trajectory joining the points of given compact sets, while minimizing a certain cost function (in gener al, nonquadratic). Due to the generality of the problem, conventional methods (e.g., dynamic programming, maximum principle, etc.) are diffi cult to apply. Thus, an approximate solution is sought by constraining control strategies to take on the structure of multilayer feedforward neural networks. After discussing the approximation properties of neu ral control strategies, a particular neural architecture is presented, which is based on what has been called the ''LInear-Structure Preserv ing principle'' (the LISP principle). The original functional problem is then reduced to a nonlinear programming one, and backpropagation is applied to derive the optimal values of the synaptic weights. Recursi ve equations to compute the gradient components are presented, which g eneralize the classical adjoint system equations of N-stage optimal co ntrol theory. Simulation results related to nonlinear nonquadratic pro blems show the effectiveness of the proposed method.