Variable-Gain Dynamic Network Is Used To Solve Nonlinear Nonconvex Optimization Problems

Nonlinear nonconvex optimization problem is a very important problem in control theory and practical application,such as robot motion planning,UAV flight control and so on.At the same time,it is difficult to achieve the ideal state of noise-free pollution in the actual implementation of hardware.Moreover,the existing literature has little research on nonlinear nonconvex optimization problems.Therefore,it is valuable to study nonlinear nonconvex problems under noise pollution.In view of the fact that the varying-parameter convergent-differential neural network(VP-CDNN)only performs convergence analysis without interference when solving nonlinear nonconvex problems,the Lyapunov theory proof and experimental simulation analysis under noise pollution are given in detail in this paper.In addition,the fixed-parameter convergent-differential neural network(FP-CDNN)model is slow in solving nonlinear nonconvex optimization problems with constraints and weak in anti-interference ability.In this paper,a new mixture varying-gain dynamic learning network(MVG-DLN)is proposed,and the Lyapunov theory is proved and compared with FP-CDNN model,which further verifies the good performance of MVG-DLN model.The main work of this paper includes the following two parts:1.According to the existing research,VP-CDNN has fast and global convergence when solving optimization problems,but it has not been studied and discussed under noise interference.Therefore,the VP-CDNN model is studied to solve nonlinear nonconvex optimization problems under noise pollution.Firstly,the strong robustness of VP-CDNN under bounded disturbance is proved by Lyapunov theory.Secondly,simulation experiments are carried out under random bounded interference,periodic square wave noise interference and periodic triangular wave noise interference,and the experimental results further verify the strong robustness of VP-CDNN.2.Aiming at the nonlinear nonconvex optimization problem with constraints,the existing FP-CDNN model is not superior in performance when there is interference and no interference.In this paper,a mixture variable-gain dynamic network model is proposed.In order to demonstrate the good performance of MVG-DLN model.Firstly,the nonlinear nonconvex optimization problem with constraints is transformed into a neural dynamic model by KKT condition and projection theorem.Secondly,the neural dynamic model is transformed mathematically to obtain a mixture variable-gain dynamic network model.Then,the convergence and robustness of the MVG-DLN model are proved by Lyapunov theory.Finally,a numerical simulation experiment comparing MVG-DLN model with FP-CDNN model is carried out,which highlights the superior performance of hybrid variable gain dynamic network model.In particular,the high-dimensional simulation is carried out,and the experimental results further verify that the MVG-DLN model still shows good convergence performance and strong robustness when solving the high-dimensional constrained nonlinear nonconvex optimization problem.