Neural Control And Deterministic Learning For Several Classes Of Discrete-Time Nonlinear Systems

The actual control system usually contains highly nonlinear and uncertain,so it is difficult to establish an accurate mathematical model for the actual control system.Adaptive neural control technology uses the universal approximation ability of neural networks(NNs)to adjust the NNs online to approximate the unknown nonlinear functions and has been regarded as an effective method to solve the control problem of the system with unknown nonlinear functions.Deterministic learning is a learning method based on adaptive neural control,which can obtain the knowledge of accurately modeling the unknown nonlinear function of the system from the stable control process.The deterministic learning method not only ensures the stability of the system,but also further ensures that the estimated NN weights converge to their ideal values,store the converged NN weights,and use the stored NN weights to construct the neural learning controller to improve the control performance.The existing deterministic learning research mainly focuses on continuous-time systems.However,with the continuous development of digital computers,the modeling,simulation,and application of actual control systems are realized on digital computers,which means that the original continuous-time system should be sampled or discretized.In addition,the unique prediction characteristics of discrete-time controllers are also the expected requirements of practical engineering systems.Therefore,the study of adaptive neural control and deterministic learning for discrete-time nonlinear systems has important theoretical significance and practical application value.In view of this,combined with adaptive neural control technology,deterministic learning method,and exponential stability theory of discrete-time linear time-varying systems,this thesis studies the deterministic learning problem of discrete-time nonlinear systems with unknown functions in the following four aspects:1)Consider the problems of adaptive neural control and deterministic learning for a class of discrete-time strict-feedback nonlinear systems.Firstly,in order to verify the exponential convergence of the estimated weights,an extended exponential stability corollary for a class of discrete-time linear time-varying systems with delays and small perturbations is given.Subsequently,by combining the n-step-ahead predictor technology and backstepping,an adaptive NN controller is constructed,which integrates the novel weight updating laws with time delays,and the controller ensures the system output tracking the given recurrent reference signal.After the system enters steady-state,combining the recursiveness lemma of smooth function and the system state equation,all the NN input variables are verified to be recurrent;and the exponential convergence of the estimated weights is verified by the extended exponential stability corollary.Then,a set of learning rules is constructed according to the convergence characteristics of estimated NN weights,which are saved as time-invariant constant NN weights by using the learning rules.Finally,the time-invariant constant NN weights are reused to construct the neural learning controller by combining a mod function,which can not only accomplish the same or similar tracking control tasks,but also greatly improve the control performance and reduce the amount of online calculation.2)Consider the problems of both state-feedback and output-feedback adaptive neural control and deterministic learning for a class of discrete-time pure-feedback nonlinear systems.Firstly,for the two cases that all system states are measurable and only system output is measurable,both state-feedback and output-feedback adaptive neural controllers are constructed by combining the classical n-step input-state predictor and n-step input-output predictor,which can ensure the system output tracking the given recurrent reference signal.After the system enters steady-state,an implicit function theorem-based non-affine function recursiveness lemma is proposed to verify that the NN input variables under the two control schemes are regression;and the estimated NN weights are verified to converge to their ideal weights under the two control schemes.Then,a set of new and simple learning rules is constructed,and the estimated NN weights are stored as constant NN weights which can accurately model the unknown system nonlinear function.Finally,the corresponding both state-feedback and output-feedback neural learning controllers are constructed by using the constant NN weights to improve the control performance and reduce the amount of online calculation.3)Consider the problems of leader-follower control and deterministic learning for a class of discrete-time multi-agent systems.Firstly,a two-layer design framework is used to solve the leader-follower control problem,in the first layer,each agent can predict the future state of the leader in a distributed way by combining the adaptive distributed observer and the constructed predictor;In the second layer,the adaptive neural controller is designed combining the predicted future signal and the deterministic learning theory to ensure the completion of the leader-follower control task.Subsequently,the convergent estimated NN weights of each agent are saved and reused to construct neural learning controllers by using the learning rules.Then,the convergence speed and convergence region of the two control schemes are given by using the logarithmic Lyapunov function,the results show that the neural learning controller has faster convergence speed and smaller convergence region than the adaptive neural controller.Finally,the proposed scheme is extended to the formation control of a multi-unmanned ship system.4)Consider the problem of cooperative deterministic learning for a class of discrete-time multiagent systems under directed and balanced graphs.Firstly,in order to handle the asymmetry of the Laplacian matrix under directed graphs,by using graph theory and matrix theory,the relationships between cooperative persistent excitation conditions and persistent excitation conditions under directed balanced graphs are established;by using the matrix null-space theory,an exponential stability lemma of a class of discrete-time linear time-varying systems with asymmetric system matrix is given.Subsequently,the adaptive neural controller and the distributed neural weight update law are designed,and the stability of the system is verified by Lyapunov theorem and matrix theory.Then,combining the null-space theory and exponential stability lemma,it is verified that the estimated NN weights of every agent can converge to the common ideal values of all agents.The proposed cooperative deterministic learning scheme enhances the NNs’ generalization domain of each agent be the union of all agents and enhances the learning ability of NNs.