Global Optimization Auxiliary Function Method For Discrete Time Optimal Control Problems And Its Application

As an important part of modern control theory,optimal control has considerable influence on improving system efficiency,optimizing resource allocation,improving economic efficiency,and reducing energy consumption.It has become an important part of energy saving and emission reduction in industrial processes.Discrete time optimal control is widely used in practical problems such as multi-stage control and scheduling.Therefore,the research about discrete time optimal control problem has gradually become a hot topic.With the global optimization continuously involved in the optimal control field,the global optimal solution using the auxiliary function method to solve the optimal control problem has attracted great interest from scholars at home and abroad.In recent years,many scholars have proposed a series of related ideas,theories and methods,which make the framework of solving optimal control problems become more and more complete.Based on the existing theoretical research,this paper mainly considers the application of the filled function method in discrete time optimal control problems.So far,the algorithm system of nonlinear programming problems is formed maturely.We attempt to use the control parameterization method to transform the high-dimensional discrete time optimal control problem into a low-dimensional nonlinear programming problem,then give rise to a suitable filled function and design a corresponding optimal algorithm.Furthermore,by considering the important influence of reputation evaluation in the development of e-commerce,we introduce an online reputation evaluation model.It is shown that we can get the optimal execution strategy.In general,the auxiliary function method is a common method for obtaining global optimization solutions.Here,we introduce several common auxiliary function methods firstly,such as the filled function method.Secondly,we can extend the second-order optimality conditions of existing nonlinear programming problems to the optimal control problem,which are based on the study of first-order optimality conditions,and then the second-order optimality conditions of discrete time optimal control problems are proposed.For the discrete time optimal control problems with and without constraints,the main idea is to construct a corresponding one-parameter filled function with continuous differentiability.After analyzing the relevant properties,a filled function algorithm isproposed and its convergence is proved.On this basis,we consider the practical problem–online reputation evaluation,and then obtain the optimal execution strategy.In other words,we present a transformation approach for transforming the optimal control problem into a nonlinear optimization problem.After the global optimization auxiliary function method,some research results are developed.Then the method proposed is applied to solve practical problems.During this,it is showed that some related algorithms have deficiencies to some degree.So the research of the global optimization of the discrete time optimal control problem still needs further investigation.