On a Stabilization Problem of Nonlinear Programming Neural Networks

Abstract Intrinsically, Lagrange multipliers in Nonlinear Programming Theory play a regulating role in the process of searching the optima of constrained optimization problems. Hence, they may be regarded as control input variables as those in control systems. From this new perspective, it is showed that synthesizing nonlinear programming neural networks can be formulated to solve servomechanism problems. In this paper, under the second-order sufficient assumptions of nonlinear programming problems, a dynamic output feedback control law is proposed to stabilize the corresponding nonlinear programming neural networks. Moreover, their asymptotical stability is proved by the Lyapunov First Approximation Principle.