Multi-dimensional Taylor Networksoptimal Tracking Control For Nonlinear Constant System

As the most common phenomenon in nature and the engineering technology,nonlinear system has always been one of the important theoretical and practical problems in the field of automatic control.The pursuit of direct control and processing method for nonlinear systems is a goal that has been pursued in the field of automatic control.Based on this problem,from the perspective of engineering implementation,this thesis aims to provide a theoretical basis for the control and application of nonlinear systems from the aspects of feedback control and parameter conditions of nonlinear systems.Multi-dimensional Taylor network(MTN)extends the high order expansion of the specified power of the input signal,and it has good approximation performance.At the same time,the MTN requires only addition and multiplication,so it is easy to realize real-time control.As a dynamic model,the MTN has a fixed structure of controller,so it can be weakened that the dependence of controller design on system model information.Based on this,for the purpose of practical application,it is discussed that problem of the application of MTN controller to different constant nonlinear systems(For the convenience of narration,the word "constant" is ignored,and nonlinear systems are used to replace constant nonlinear systems).For the single input single output(SISO)nonlinear system,multi input multi output(MIMO)nonlinear system and nonlinear system modeling problems,it is studied the specific problems that the MTN controller basic structure,input composition,parameter selection and adjustment algorithm.It has done a preliminary study on the applicability and implementation of nonlinear system controller in this dissertation.The main contributions of this thesis can be summarized as follows:1.For single input and single output nonlinear system control,on the basis of the original MTN,with the control input item added to the nonlinear dynamic model,MTN optimal feedback controller is proposed in this dissertation and the validity of the MTN basic structure is proved.Based on this,the weight parameters training algorithm of the controller with the input term is given by the conjugate gradient method.And it is given that the basic algorithm to select the initial value of the controller parameters by the principle of minimum value.Using the linear combination of the input and its high power product,it is easy to be realized on a computer.In addition,the dependence on the system model can be effectively reduced,and the complexity of the calculation is greatly reduced.Despite the errors in the modeling process,MTN optimal controller manages to stabilize the system for tracking the desired output,and it is also given that the design process of the MTN controller.Finally,the experimental results show the effectiveness of the proposed method by numerical simulation.By realizing the optimal closed-loop tracking control of the SISO nonlinear system by output feedback,MTN controller guarantees its real-time control accuracy,dynamic performance,robustness,and anti-disturbance capability.2.It is studied that a MTN output feedback tracking control of SISO nonlinear systems in discrete-time form.Target of SISO nonlinear system with model unknown,a novel approach based on the MTN controller is proposed.By using Lyapunov analysis,it is proven that output signals in the closed-loop system are remain bounded and the tracking error converges to an arbitrarily small neighborhood around the origin.It is also proposed that an identification method based on MTN,not needing to know about the mechanism model structure of the actual system for MTN,as a dynamic model,can be taken as a system model to approximate any nonlinear dynamic model.Parameters of the real system are reflected in the adjustment process of its weights.The implied characteristics can be clarified by the input and output data of MTN.The output of the real system can be approached only by adjusting the internal weights.Finally,the experimental results show the effectiveness of the proposed method by numerical simulation.3.The actual controlled object is generally a MIMO nonlinear system,and its model is often inaccuracy or even unknown.Considering MIMO nonlinear systems in engineering which the input is in the form of nonlinear coupling,the problem of asymptotic tracking and dynamic adjustment of the system is studied.And a new control scheme based on MTN controller is proposed.It proves that the tracking error converges to an arbitrarily small neighborhood around the origin when certain conditions are met.The control target is implemented that for the MIMO nonlinear systems,design the adaptive MTN optimal output feedback controller to make the nonlinear system stable,enabling its output to track the desired signal and its parameters and tracking error to be uniformly bounded.At the same time,the parameter adjustment algorithm of the controller does not require the controlled object specific parameters.And it is given that a general process to get the parameters of the controller.Finally,the experimental results show the effectiveness of the proposed method by numerical simulation.During the experiment,the MTN controller tracks the desired output curve satisfactorily.4.Considering MIMO nonlinear uncertain discrete system,it is proposed that the adaptive output feedback controller based on MTN for MIMO nonlinear system.By Lyapunov function,it is proved that all the output signals of the closed loop system are the semi-globally uniformly ultimately bounded and the output errors converge to a compact set.These systems are of couplings in every equation of each subsystem,and the different subsystems may have different orders.As a kind of dynamic system,MTN can be considered as a system model.In addition,MTN requires only addition and multiplication,so it is easy to realize real-time control.Due to the reduction of the computational complexity of the controller,the real-time performance in the control process has been greatly improved.More than that,MTN optimal controller has better dynamic characteristics.And the adaptive adjustment algorithm is proposed here.It is also given that the general process of the design of MTN controller.Finally,by a numerical simulation,the experimental results show that the MTN controller can not only make the system track asymptotically the known object,but also optimize system performance remarkably.