On a Stabilization Problem of Nonlinear Programming Neural Networks

• Published in: Neural processing letters Vol. 31; no. 2; pp. 93 - 103
• Main Author: Huang, Yuancan
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01.04.2010; Springer; Springer Nature B.V
• Subjects: Algorithms; Applied sciences; Artificial Intelligence; Complex Systems; Computational Intelligence; Computer Science; Computer science; control theory; systems; Connectionism. Neural networks; Control theory; Exact sciences and technology; Feedback control; Lagrange multiplier; Neural networks; Nonlinear programming; Output feedback; Servomechanisms; Recurrent neural network; Servomechanism; Stability; Recurrent neural nets; Recurrent neural networks; Stabilization; Lyapunov method; Nonlinear problems; Non linear programming; Neural network; Constrained optimization; Equilibrium point; Lagrange multiplier; Optimal solution; Problem solving; Dynamic programming; Lyapunov function; Mathematical programming
• ISSN: 1370-4621; 1573-773X
• DOI: 10.1007/s11063-010-9129-x

Intrinsically, Lagrange multipliers in nonlinear programming algorithms play a regulating role in the process of searching optimal solution of constrained optimization problems. Hence, they can be regarded as the counterpart of control input variables in control systems. From this perspective, it is demonstrated that constructing nonlinear programming neural networks may be formulated into solving servomechanism problems with unknown equilibrium point which coincides with optimal solution. In this paper, under second-order sufficient assumption of nonlinear programming problems, a dynamic output feedback control law analogous to that of nonlinear servomechanism problems is proposed to stabilize the corresponding nonlinear programming neural networks. Moreover, the asymptotical stability is shown by Lyapunov First Approximation Principle.