Multi-dimensional Taylor Network Identification And Predictive Control For Nonlinear Time-delay Time-invariant Systems

Most industrial systems are of the characteristics of nonlinearity,time-delay and coupling,and influenced by external disturbance,which may lead to the large overshoot and the long adjusting time,so that the transition process of the system may deteriorate and the stability is reduced,even easy to result in the instability of the closed-loop system.How to overcome these problems and effectively control the system has become the research focus in the field of control theory and engineering.On the one hand,it is difficult to build a precise model because of the characteristics of time-delay and nonlinearity.On the other hand,some results on the linear system are difficult to apply to the nonlinear system.Recently,Multi-dimensional Taylor Network(MTN)provides an effective solution for nonlinear system modeling and control,which has simple structure,fast computation speed,parallel processing,independent learning and strong nonlinear mapping ability.MTNs are applied to the nonlinear time-delay systems to solve the problems,such as nonlinearity,time-delay,coupling and external disturbance,etc.Therefore,the research of this subject has important theoretical significance and practical application value.In this dissertation,the nonlinear time-delay time-invariant systems(record briefly nonlinear time-delay systems)are treated as the research object,and the external disturbance,noise,coupling and input dead zone are taken into consideration synthetically.The MTN as a research tool which combined with the idea of predictive control is used to research control of nonlinear time-delay systems.The dynamic characteristic and the computational complexity are improved as the core and the key,respectively.By the excellent performance of MTN,MTN identification model,MTN predictive model,MTN controller and MTN compensator are designed,respectively.The tracking control problem of nonlinear time-delay systems is researched in depth,and predictive control schemes based on MTN are proposed.Meanwhile,the stability of the closed-loop system is proved by Lyapunov stability theory.The main contributions are summarized as follows:1.The identification scheme of nonlinear time-delay system based on MTN is proposed.MTN is used to identify the nonlinear time-delay system,and the rationality of MTN model is proved.Establish the ordering of weighting terms in the model and their recursive expressions.Optimal MTN identification model is obtained according to the relationship of middle layer's nodes and output weights value using MTN's special structure and Extreme Learning Machine(ELM)algorithm,and ELM algorithm is used to calculate the output weights value and avoided iterative optimization process of gradient method.On the premise of guaranteeing the operation precision,it effectively reduces the algorithm's complexity.Combined with the pruning algorithm,the structure of MTN is simplified to improve its computation efficiency.By means of cross correlation function,the unknown time delay is identified by correlation of input and output signals.Experimental results verify the effectiveness of the proposed scheme.2.The predictive model construction scheme of nonlinear time-delay system based on MTN is proposed.Based on the nonlinear approximation performance of MTN,two schemes of constructing predictive models,the recursive and non-recursive MTN predictive model,are proposed to compensate the influence of time-delay.Moreover,real-time online modeling with appropriate learning algorithms can accurately construct the predictive model so that compensates the influence of time-delay.Experimental results verify the effectiveness of the proposed scheme.3.The predictive control scheme and stability proof scheme of single input and single output(SISO)nonlinear time-delay system based on MTN are proposed.Without state feedback,the real-time output tracking control of the system relative to the given reference signal is realized by the closed-loop control only relying on the output feedback.Based on the nonlinear approximation performance of MTN,a non-recursive d-step-ahead MTN predictive model is designed to compensate the influence of time-delay.MTN controller is designed to realize accurate tracking control of the system.Using the network structure of MTN controller,the error signal synthesized by input signal and output signal is used as the controller input.According to Lyapunov stability theorem,the stability of closed-loop system is proved.Experimental results verify the effectiveness of the proposed scheme.4.The predictive control scheme and stability proof scheme of SISO nonlinear time-delay system without external disturbance and with external disturbance based on MTN are proposed.MTN is treated as predictive model,controller and compensator to realize real-time output tracking control of the system relative to a given reference signal without state feedback.Based on the nonlinear approximation performance of MTN,a non-recursive d-step-ahead MTN predictive model is designed to compensate the influence of time-delay.MTN control law is designed for output tracking control of nonlinear time-delay systems.At the same time,MTN compensator is established to compensate the influence of external disturbance.The stability of closed-loop system is proved according to the Lyapunov stability theorem.Based on that,the adjustment method of MTN controller parameters is obtained using the predictive accuracy of MTN model,control coefficient and optimal coefficient.Experimental results verify the effectiveness of the proposed scheme.5.The predictive control scheme and stability proof scheme of multiple input and multiple output(MIMO)nonlinear time-delay system based on MTN are proposed.It can realize the real-time output tracking control of the system relative to the given reference signal by virtue of the good characteristics of MTN,which has good generalization performance,without decoupling process and state feedback.The recursive d-step-ahead MTN predictive model is designed by the recursive technique.According to the characteristics of MTN structure,MTN controller is designed to realize accurate tracking control of the system,and the error signal synthesized by input signal and output signal is adopted as the input of controller.The stability of closed-loop system is proved by the Lyapunov stability theorem.Experimental results verify the effectiveness of the proposed scheme.6.The predictive control scheme and stability proof scheme of MIMO nonlinear time-delay system with unknown time-delay based on MTN are proposed.Based on identification of the time-delay,a recursive d-step predictive control scheme based on MTN is proposed.The recursive d-step-ahead MTN predictive model is designed by using the recursive technique.The multi-step predictive objective function is given.The optimal control law is obtained by iterative refinement.The stability of closed-loop system is proved according to the Lyapunov stability theorem.Based on that,the adjustment method of MTN controller parameters is obtained using the predictive accuracy of MTN model,control coefficient and optimal coefficient.Experimental results verify the effectiveness of the proposed scheme.