Adaptive Control For Nonlinear Uncertain Systems Based On Expanded Neural Networks

In the practice of current automation engineering,the intellectualization of information transmission and system control has become one of the main features in the field of control science and engineering research.Especially,it is a research direction in this field that intelligent systems are utilized to approximate uncertainties in nonlinear functions.Therefore,the research on the control design based on intelligent system has important scientific and engineering practical singificance for nonlinear uncertain systems.In the field of control science and engineering research,artificial neural network is a kind of important intelligent system.Its main aim is to accomplish certain target tasks by imitating the operation and logic function of the intelligent biology neuron network.At present,the artificial neural networks methods have been widely studied and applied to system modeling,parameter identification,pattern recognition and control design.It is worth noting that the topological layout of hidden layer neurons and the update laws of neurons' weights are still the criterions for measuring the performance of artificial neural networks.In the field of control theory research,the existing results show that artificial neural networks can approximate any continuous nonlinear function.However,in the practical application,it is still an open problem to solve how to distribute the hidden layer neurons(topological structure)for improving computational efficiency.The existing research results propose many valuable learning laws of weights in the artificial neural networks.However,in the control system design,because of a large number of neurons,the online updating of the weights often make the computational complexity increasing dramatically,which causes the system unstable.To solve the above problems,an expanded neural network is proposed for a class of nonlinear uncertain systems in this paper.The main idea is to build expanded neural networks which composed of normal neural networks,saturators and scalers with adjustable parameters.The expanded neural networks are used to approximate the uncertainties in the nonlinear systems.In the control process,the weights of neural networks are trained off-line,only the adjustable parameter of the scaler is updated online.Therefore,this control scheme can effectively reduce the online computation burden arised from the online updating of the weights.On the other hand,by using the partition of unity in differential geometry,a new artificial neural network is proposed in this paper.The state domain of network neurons is proposed to layers and groups the hidden neurons.Then a hidden layer structure with hierarchical nesting is formed.In the operation of the network,this structure can effectively activate neurons in the state domain while other neurons outside of the state are not activated.Therefore,the above nested neural network can reduce the computational burden.By combining the expanded neural networks method with the nested neural networks,an adaptive neural control design is proposed for a class of uncertain nonlinear systems.The main work and research results of this thesis are shown as follows:(1)The research background and the significance of the thesis are introduced.Research on artificial neural networks and several classical control methods for nonlinear systems are presented.Finally,some necessary research topics are also proposed.(2)Based on the universal approximation property of neural network,an adaptive nerual tracking control design algorithm with supervisory control is proposed for a class of nonlinear uncertain systems.The content of this chapter can be regarded as the inspiration and guidance of this thesis.The idea of supervisory control inspires the author to propose expanded neural networks and nested neural networks.(3)Combining off-line training with on-line adjustment,an adaptive neural control design with scalers and saturators is proposed for a class of SISO uncertain nonlinear systems.In the off-line training,the structures of neural networks are trained to approximate the unknown functions of nonlinear systems.After the training,the network's parameters remain unchanged.Then in the on-line adaptive control,the factor of the scaler and the estimate parameters of neural approximation accuracy are adjusted in the closed-loop dynamic system.The advantagement of the method is that the control process are divided into two parts which include off-line training and on-line adjustment.In the off-line training,any kind of neural networks which have approximation ability can be used to estimate the uncertainties of nonlinear systems.In the on-line adjustment,only the factor in the scaler and several estimate parameters of neural approximation accuracy are to be adjusted,which means the number of updated on-line parameters is less.By using the Lyapunov stability theory,the control scheme proposed in this paper may guarantee that all the signals in the closed-loop system are uniformly ultimately bounded(UUB).(4)The nested BP neural network is proposed.Firstly,a concept of "state domain" is definited.And then the "state domain" and the partition of unity are utilized to activate the neurons falling into the "state domain".The advantagement of the nested BP neural network is that the number of neurons can be reduced which means the learning efficiency is improved.Secondly,by applying the Lyapunov stability theory,an adaptive neural tracking control scheme is presented for a class of uncertain nonlinear systems.The expanded neural networks with scalers and saturators are used to synthesize the controller which guarantees that all the signals in the closed-loop system are uniformly ultimately bounded(UUB).Compared with existing adaptive neural control schemes,the proposed scheme can reduce the number of training neurons and updated on-line parameters,which means the burden of computation is greatly reduced.