Multi-layer neural networks for the solution of generalized nonlinear terminal control problems

The authors deal with the problem of designing closed-loop feedforward control strategies to drive the state of a dynamic system from any point of a given initial set to any point of a given target set so as to minimize a certain cost function. An approximate solution is sought by constraining control strategies to take on the structure of multilayer feedforward neural networks. The approximation properties of neural control strategies are discussed, the terminal control problem is extended to the state-tracking control problem, and a particular neural architecture is presented. The original function problem is then reduced to a nonlinear programming one, and backpropagation is applied to derive the optimal values of the synaptic weights. Recursive equations to compute the gradient components are presented, which generalize the classical adjoint system equations of N-stage optimal control theory