【作者】 张超；

【导师】 严洪森；

【作者基本信息】 东南大学 ， 控制理论与控制工程， 2018， 博士

【摘要】 作为工程技术中最为普遍的现象,非线性系统的稳定性分析和控制器设计具有重要理论价值和现实意义。寻求一种简单、直接对非线性系统进行控制和处理的方法,是自动控制领域一直追求的目标。本文立足于这一问题,从工程实现角度出发,以稳定性证明为基础,以提高动态性能为核心,以改善计算复杂度为关键,旨在为多维泰勒网(MTN)在非线性系统中的应用研究提供一定理论基础。尽管在非线性系统控制领域取得了丰硕的研究成果,但其大都缺乏对耦合、不确定性、时变特性以及测量噪声的综合考虑。而如何在确保实时性能的前提下将系统耦合、随机因素、时变特性和不确定非线性的影响一同最小化是具有重要意义的。近年来,MTN优化控制方法已广泛应用于非线性系统的控制中,为非线性系统控制器设计和稳定性分析提供了新的解决方案。本文利用多维泰勒网优良特性,结合系统辨识、自适应控制和非线性滤波等方法,对几类具有噪声干扰的非线性时变系统的跟踪控制问题进行了深入研究,提出了基于MTN的综合优化控制策略,并采用Lyapunov稳定性理论,证明闭环系统的稳定性。论文的主要研究工作概括如下:1.为解决含噪声单输入单输出(SISO)非线性时变系统实时跟踪控制问题,提出了基于MTN的逆控制方案,其中三个MTN分别作为:实现逆建模的自适应逆控制器、系统建模的自适应模型辨识器和噪声干扰消除的非线性滤波器。在该方案中,为了避免“折衷”,将对象的动态响应控制和消除干扰的控制分成两个独立的过程进行,同时实现最优控制。此外,采用改进的权衰减法选择有效回归项来避免维数爆炸,克服了传统神经网络需提前确定中间节点数的缺点。经过一定的训练后,精简的MTN更有助于满足软件实现和工程应用的实时性要求。为在理论上确保MTN逆控制的严谨性,证明了SISO非线性逆系统存在的一般条件以验证方案的可行性。仿真结果验证了方案的有效性。2.针对含噪声SISO不确定非线性时变系统,提出一种基于MTN稳定的自适应控制方案。首先,MTN滤波器(MTNF)用来消除干扰和测量噪声,以得到无随机干扰的模型输出。然后,MTN辨识器(MTNI)用来表示系统动态映射且比传统神经网络泛化能力更强。而后,MTN控制器(MTNC)用来实现系统精确跟踪控制,其中不确定非线性时变系统由MTNI辨识并将对象动力学特性信息提供给MTNC使其“光滑”自适应。此外,利用改进的灵敏度计算方法来剪除MTNI和MTNC的冗余输入和冗余中间层回归项以得到精简的MTN网络,达到减少迭代学习的计算复杂度和利于工程实践的目标。最后,通过Lyapunov稳定性理论,证明基于MTN的闭环系统稳定性,并给出最优学习率以实现快速学习。仿真结果表明,该方法具有精确的辨识能力、良好的跟踪性能和较强的抗干扰能力,可以实现含有不确定性、随机因素和时变特性的非线性系统自适应实时控制。3.提出了一种基于多输入多输出(MIMO)MTN的自适应控制方案,用于实时跟踪控制含噪声MIMO不确定非线性时变系统,其中两个MTN分别被用来实现优化控制和非线性滤波。首先,提出了MIMO MTNC来实现精确的跟踪控制,将滤波输出和期望值之间的闭环误差作为MTNC的输入。根据系统不确定因素和快时变特性引起的误差,利用弹性BP算法和线性再励的自适应变步长算法来在线快速地更新MTNC权值,证明了能够保证闭环系统稳定的学习率。其次,提出了MIMO MTNF来消除测量噪声等随机因素。由于定义了测量值和MTNF输出之间误差的Lyapunov函数,自适应MTN滤波系统兼具基于Lyapunov理论的自适应滤波(LAF)和MTN的特有性质。通过在Lyapunov意义下选取适当的权值更新律,MTNF输出可以渐近地收敛到期望信号,并且LAF MTN滤波器独立于输入干扰的随机特性。根据Lyapunov稳定性理论,证明了滤波器的收敛性和稳定性。最后,仿真表明方案具有良好的跟踪能力和抗干扰能力,与基于径向基神经网络的方案相比,控制性能改善明显。同时,基于MIMO MTN的控制方案在实时性要求较高的应用中也很有前景。4.在前述含噪声SISO/MIMO不确定非线性时变系统MTN跟踪控制问题研究的基础上,进一步研究了综合考虑系统耦合、随机因素、快时变特性和不确定非线性的性能优化问题,提出了一种基于MIMO MTN的优化控制方案。首先,引入直接逆建模方法来初始化MTNC权值,以提高收敛速度和避免陷入局部最小。设计基于强化学习和自适应动量因子的改进梯度法来调节MTNC权值以快速响应被控对象的不确定性和快时变特性,实现最优控制。证明了闭环系统的稳定性。而后,通过Lyapunov稳定性理论设计MTNF权值更新律,使动态误差指数收敛到零。恰当选择Lyapunov函数来构造具有全局最小值的能量空间并对MTNF的Lyapunov特性进行分析。证明MTNF误差的收敛速度和收敛区域,避免奇点问题。最后,对含强耦合、不确定性、快时变特性以及测量噪声等随机因素的复杂MIMO非线性系统进行仿真实验,结果表明,所提出的控制器和滤波器可以在较短的时间内获得更高的精度。更多还原

【Abstract】 As the most common phenomenon in the engineering technology,the stability analysis and controller design of nonlinear systems have the important theoretical value and practical significance.The pursuit of a simple direct control and processing method for nonlinear systems is a goal that has always been pursued in the field of automatic control.Based on this problem,from the perspective of engineering implementation,this thesis is based on the stability proof,takes the improvement of dynamic performance as the core and focuses on the improvement of computational complexity as the key.The purpose is to provide a theoretical basis for the application of the multi-dimensional Taylor network(MTN)in nonlinear systems.Although there are several developments on the control of nonlinear systems,they do not involve the overall consideration of the coupling,uncertainty,time-varying characteristics and measurement noise commonly.How to minimize the influence of system coupling,randomness,time variation and uncertain nonlinearity together and how to improve the real-time performance are of great significance.In recent years,MTN optimal control method has been widely used in nonlinear control systems,which provides a new solution for systematic design and stability analysis of nonlinear systems controllers.Using the MTN’s excellent properties,this dissertation is devoted to propose the MTN based control scheme to address the problems of tracking control for several classes of nonlinear time-varying systems with noise disturbances by combining the approaches of system identification,adaptive control and nonlinear filtering,etc.Moreover,the stability of the closed-loop systems is proved by employing Lyapunov theory.The main contributions of this thesis are summarized as follows:1.An inverse control scheme based on MTN is proposed for the real-time tracking control of single-input/single-output(SISO)nonlinear time-varying systems with noise disturbances.Utilized in this scheme are the three MTNs: the adaptive model identifier for system modeling,the adaptive inverse controller for inverse modeling,and the adaptive nonlinear filter for eliminating the noise disturbance.To avoid “compromise”,this scheme is designed into a structure wherein controlling the object dynamic response and eliminating the noise disturbance are divided into two relativelyindependent processes.Furthermore,the weight-elimination algorithm is adopted for choice of effective regression items to avoid the dimension explosion,thus overcoming the shortcoming that the number of middle nodes needs to be determined before using the traditional neural network.After a certain number of training,the more streamlined MTNs are observed to contribute to satisfying the real-time requirements of software implementation and engineering application.To ensure that MTN inverse control is strict in theory,the general conditions for the existence of SISO nonlinear inverse systems are identified.Simulation of the MTN inverse control is conducted to confirm the effectiveness of the control scheme.2.A stable adaptive control approach based on MTN is proposed to control the SISO uncertain nonlinear time-varying systems with noise disturbances.Firstly,an MTN filter(MTNF)is developed to eliminate the control interference and measurement noise,so that the model output without stochastic disturbance can be obtained.Then,an MTN identifier(MTNI)is so designed as to be capable of dynamic mapping and require fewer weights than traditional neural networks.On the basis of the above,the feed-forward MTN controller(MTNC)is developed to realize the precise tracking control of the system.The uncertain nonlinear time-varying system is identified by MTNI,which then provides sensitivity information of the plant to MTNC to make it adaptive.Furthermore,the skeletonization algorithm is adopted to remove redundant inputs and redundant regression items from MTNI and MTNC for concise MTNs.Successful convergence and faster learning are guaranteed using the Lyapunov theorem,and the optimal learning rates are identified.Simulation results demonstrate that the proposed approach features its accurate identification,excellent tracking and better anti-interference capability for the adaptive real-time control of uncertain,stochastic and time-varying nonlinear systems.3.An adaptive control approach based on multi-input/multi-output(MIMO)MTN is presented for tracking control of MIMO uncertain nonlinear time-varying systems with noises in real time,where two MTNs are proposed to formulate the optimal control and nonlinear filtering approaches.Firstly,the MIMO MTNC is proposed to realize the precise tracking control.The closed-loop errors between directly measured outputs(which have been filtered)and expected values are chosen to be the MTNC’s inputs.The proposed MTNC can update its weights online according to errors caused by system’s uncertain factors and fast time-varying characteristics.The stability of closed-loop system is proved based on stable learning rate.The resilient back-propagation algorithm and adaptive variable step size algorithm via linear reinforcement are utilized to update the MTNC’s weights.Secondly,the MIMO MTNF is proposed to eliminate measurement noises and other stochastic factors.The proposed adaptive MTN filtering system possesses the distinctive properties of the Lyapunov-theory-based adaptive filtering system and MTN,where a Lyapunov function of the errors between the desired signals and the MTNF’s outputs is first defined.By properlychoosing the weights update law in the Lyapunov sense,the MTNF’s outputs can asymptotically converge to the desired signals.The LAF MTN filter is independent of the stochastic properties of the input disturbances.The convergence and stability are proved by the Lyapunov stability theory.Finally,the simulation demonstrates excellent tracking ability and better anti-disturbance capability with improved control performance over that of RBF neural network.And the results show that the MTN based control system is very promising for real-time applications.4.Based on above three contents,to further explore the performance optimization considering system coupling,randomness,fast time variation and uncertain nonlinearity,an effective MIMO MTN based optimal control scheme is presented.Firstly,the direct method of inverse modeling is introduced to initialize the MTNC for improving the convergent speed and preventing weights trapping into local optima.To adapt the initially uncertain and fast time-varying parameters in the control system,we introduce an improved gradient descent method to adjust the MTNC parameters.The stability of our closed-loop system is proved according to the Lyapunov method.Secondly,MTNF weight adaptation scheme is designed based on the Lyapunov stability theory to iteratively update the weights.In the design,the Lyapunov function has to be well selected to construct an energy space with a single global minimum.Analysis and discussion on Lyapunov properties of the proposed MTNF are included.Finally,the simulation of complex nonlinear MIMO system is presented with strong coupling,uncertainty,fast time-varying characteristics,measurement noises and other stochastic factors.Empirical results illustrate that the proposed controllers can obtain good precision with shorter time compared with the other considered methods.更多还原