Research On Bounded-Error Modeling With Parameters Optimization Of Interval Neural Networks

Whether to design a controller of a system or to study the control theory,we must build a system model at first.Actually,control systems are usually running in a constantly changing environment,so there is uncertainty in the system.In order to deal with the uncertainty,we must incorporate it into the system model.For an uncertain system,the errors produced by measurement and modeling are usually unknown but bounded,that is,the error is considered to be in an interval bound,so this kind of problem is called a bounded error problem.It is of great significance to study how to build a model of bounded error problems for the analysis of actual control systems.This paper mainly studies a modeling method of bounded error with optimizing parameters of interval neural networks.This method combines the traditional neural network with interval analysis theory to construct an interval neural network with interval weights and thresholds to complete the modeling of bounded error problems.Since the learning process of neural network is the process of parameter optimization,and the traditional gradient descent method is easy to fall into local optimum,this paper proposes an interval particle swarm optimization algorithm as the learning method of interval neural network.The methods proposed in this paper includes both single and multiple objective functions in order to build the models of the known and unknown error bounds respectively.The proposed methods are applied to the modeling of various control systems.The results show that the single-objective modeling method has a good fitting effect for the problem of known error bounds,and the multi-objective modeling method has a good fitthing effect for the problem of unknown error bounds.In addition,the networks constructed have good dynamic characteristics.The main work of this paper is as follows:(1)Introduce the interval analysis theory,point-valued particle swarm optimization algorithm,basic principles of neural networks,the bounded error problem and system modeling method based on such problem.(2)Propose a single-objective interval particle swarm optimization algorithm to evolve interval neural networks offline,so as to build the model of the bounded error problem.Through numerical simulation experiments,we find that the proposed method has a good fitting effect on the known-bounded error,but fails in the unknown-bounded one.(3)Propose a multi-objective interval particle swarm optimization algorithm to evolve interval neural networks offline,which includes the selection and ordering of the interval noninferior solution sets,selection of the individual historical optimal position and the global one,the particle variation and the selection of the optimal value within the Pareto frontier.The interval neural network is trained based on the proposed multi-objective algorithm to complete the modeling.The numerical simulation experiment shows that this method can model the unknown-bounded error problem and has a good fitness,which makes up for the shortcomings of the interval neural network modeling method based on single-objective interval particle swarm optimization algorithm.(4)The proposed methods are applied to the bounded error modeling of linear and nonlinear systems.The simulation results show that the single-objective method can build the model of known-bounded error problem,and the multi-objective method can build the model of unknown-bounded error problem.In addition,the constructed interval neural networks have good dynamic characteristics.