DRDNN: A robust model for time-variant nonlinear optimization under multiple equality and inequality constraints

Abstract

External disturbances ubiquitously exist in time-variant problems, including the time-variant nonlinear optimization problems. To develop feasible neural network for time-variant nonlinear optimization restricted to multiple equality and inequality constraints is a bottleneck problem due to its high complexity. In this paper, a novel disturbance rejection dynamic neural network (DRDNN) is proposed to handle nonlinear optimization with multiple equality and inequality constraints concerning external disturbances. According to Lagrange multiplier rule and Karush–Kuhn–Tucker condition, the original optimization problem restricted to multiple equality and inequality constraints is firstly transformed into a time-variant dynamic equation set. Then, detailed design process of the DRDNN model is developed accordingly. The proposed DRDNN inherently possesses the effectiveness and robustness by leveraging the time-derivative as well as the time-integration information. Theorems and proofs about stability, convergence property, and robustness against different forms of disturbances are provided. Finally, different examples, comparisons as well as tests substantiate the accuracy, superiority and robustness of DRDNN for nonlinear optimization limited by multiple equality and inequality constraints in disturbed scenarios.