Research Of Dynamic Optimization Approaches Based On Neural Networks

Nonlinear optimization problems can be found in scientific computation,engineering,economy and so on.There are two kinds of nonlinear optimization problems: the nonlinear optimal control problem and the nonlinear programming problem.Nonlinear optimal control means controlling a nonlinear-dynamic system and minimizing its cost function;nonlinear programming means finding the optimal value of a static nonlinear function with constraints.This thesis studies two kinds of dynamic optimization approaches based on neural networks:neural dynamic programming method and neurodynamic optimization method.In this thesis,the improved neural dynamic programming(NDP)algorithm and the event-triggered adaptive optimal control are studied for the nonlinear optimal control problem;the neurodynamic optimization method is studied for nonlinear programming problem with non-convex or non-differentiable objective function.The main contents of this thesis are as follows:1.An improved NDP algorithm is proposed to solve the approximate optimal control problem for a class of partially unknown nonlinear affine systems.This algorithm can overcome the difficult from slow changes of unknown parameters.Firstly,the relationship between optimal control and optimal cost function is clarified.Then,a simplified neural network model is used to approximate the cost function,and using NDP method to solve an approximate solution of the optimal control problem.On the basis of predecessors,the move-data window recursive least square is derived to further improve NDP algorithm,which overcomes the problems from calculation difficulty and partially unknown of system.In addition,taking Van der Pol oscillator as an example,the initial control strategy of Van der Pol oscillator is designed.The results of simulation show that the improved NDP algorithm has superior performance when the system parameters are partially unknown,and it can overcome the slow changes of parameters.2.For a class of continuous-time nonlinear affine system,this thesis proposes an event-triggered adaptive optimal control algorithm based on an encoding mechanism with limited channel transmission rate.Compared with general event-triggered control,the proposed control structure not only reduces the frequency of control,but also reduces frequency of measurement.It is proved that the encoding mechanism can achieve higher quantization accuracy with limited channel transmission rate.The control algorithm and triggering condition are studied.The proposed algorithm uses neural networks to approximate the cost function,then solves the approximate optimal control strategy corresponding to the approximate cost function.Finally,it is proved that the closed-loop system is asymptotically stable.Two examples are used to show the effectiveness of the proposed algorithm.3.For a class of non-convex programming problems with inequality constraints,this thesis proposes a new quantum-behaved neurodynamic swarm optimization(QNSO)approach.Firstly,the nonlinear optimization problem with inequality constraints is given,and a high-performance recurrent neural network is proposed.The neural network is proved to converge to the local optimum of nonlinear programming problem.Then,combined with quantum-behaved particle swarm optimization algorithm,the QNSO algorithm is designed.The performance of proposed approach is evaluated by two numerical simulations.The superiority and practicability of the proposed method are verified by two applications.4.A new projection neural network is proposed to solve a class of non-differentiable and pseudo-convex programming problems.Firstly,a new projection neural network is designed by introducing the concept of smooth function,and the circuit diagram of the proposed neural network is given.Secondly,it is proved that the states of the projection neural network are bounded.Furthermore,the projection neural network is proved to converge to the optimal solution of the pseudo-convex objective function with constraints.Two examples show the effectiveness of the proposed projection neural network.