非线性动态系统的稳定性和鲁棒控制理论研究
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摘要
随着科学技术的迅猛发展,系统对象或过程在结构、规模上变的复杂化、大型化.这就难以获得系统精确的数学模型.因此对不确定非线性动态系统的研究具有重要的理论意义和迫切的实际需要.本论文主要研究非线性动态系统模型的稳定性和鲁棒控制问题.研究工作主要集中在三个方面:首先,讨论了非线性动态神经网络系统的稳定性性质;然后,研究了非线性刚性机器人系统的鲁棒控制问题;最后,讨论了一类非完整移动机器人系统的鲁棒控制问题.本文内容共分为以下三个部分:
第一部分主要研究了非线性动态神经网络系统的稳定性性质.首先,简单回顾了神经网络的发展历史以及稳定性理论的相关研究进展.其次,研究了一类带区间不确定性的不连续神经网络系统的全局鲁棒稳定性,利用Lyapunov-Krasovskii稳定性方法,首次给出了带区间不确定性的不连续型神经网络系统全局鲁棒稳定的充分条件.随后,研究了一类带范数有界不确定性的不连续神经网络系统的全局鲁棒稳定,并给出了基于线性矩阵不等式的系统全局鲁棒稳定条件.然后,通过利用线性矩阵不等式(LMI)技术和Filippov理论,给出了一类带区间不确定性的不连续神经网络系统的全局鲁棒稳定条件.最后,介绍了机器人补偿控制中的神经网络模型及其应用.
第二部分深入研究了非线性刚性机器人系统的路径跟踪鲁棒控制问题.首先,简单叙述了机器人的发展历史,详细介绍了刚性机器人系统路径跟踪问题的研究进展和智能控制理论在机器人中的应用.接着,介绍了刚性机器人的动力学模型和相关性质,并给出了研究所需的相关数学基础.然后,研究了一类刚性机器人系统的智能混合轨迹跟踪控制.通过结合PD+前馈控制器和智能鲁棒补偿器,使得刚性机器人系统具有较强的抗干扰能力和良好的鲁棒跟踪性能.其次,分析了一类刚性机器人系统智能鲁棒H_∞控制问题.控制策略基于Lyapunov稳定性理论,结合计算力矩控制器和神经网络鲁棒控制器,保证了刚性机器人系统的鲁棒H_∞跟踪性能.最后,我们分析了一类带时滞的刚性机器人系统神经网络鲁棒跟踪控制问题,利用神经网络来逼近机器人系统的未知不确定部分,使得控制系统具有较强的自适应能力和跟踪性能,并基于线性矩阵不等式技术和Lyapunov稳定性理论,得到了跟踪误差闭环系统的鲁棒稳定性条件.
第三部分针对一类非完整移动机器人系统的路径跟踪鲁棒控制问题进行了深入研究.首先,结合现代控制技术,详细介绍了非完整移动机器人系统路径跟踪问题的研究进展和智能控制理论在移动机器人中的应用.然后,介绍了移动机器人的动力学和运动学建模.接着,研究了基于小波神经网络的非完整移动机器人系统的智能鲁棒控制问题.控制策略采用了运动控制器和自适应小波神经网络控制器相结合的办法,利用小波神经网络来逼近非完整机器人系统的未知动力学部分,同时采用一个鲁棒控制器来补偿小波神经网络的逼近误差和外部干扰,设计了小波神经网络的在线学习算法,保证了权值自适应率的收敛性和跟踪误差闭环系统的鲁棒稳定性.
论文最后总结了全文的主要创新研究成果,并对下一步研究工作进行了展望.
Along with the development of science and technology, the system object or process become larger and more complex in structure and scale than ever. Therefore, it is hard to get the accurate mathematic model of the system. In this way, it is very important to research the uncertain nonlinear dynamic systems for the purpose of theory significance and practical needs. This paper mainly deals with the study of stability and robust control for several kinds of nonlinear dynamic systems. Our research work mainly boils down to the following three parts: firstly, we discuss the stability of nonlinear dynamic neural network systems, and then, we work on the problem of trajectory tracking robust control for nonlinear rigid robot systems, finally, we discuss the problem of trajectory tracking robust control for a kind of nonlinear nonholonomic mobile robot system. The content of this paper can be listed as following three parts.
The first part mainly deals with the study of stability for nonlinear dynamic neural network systems. At first, we brief introduce the history of neural networks and the research progress of stability theory, and then, we examine the global robust stability of delayed neural networks with discontinuous activation functions and interval uncertainties. Based on the Lyapunov-Krasovskii stability method, we originally give the sufficient conditions for the global robust stability of delayed neural networks with discontinuous activation functions and interval uncertainties. Secondly, we analyze the global robust stability of delayed neural networks with discontinuous activation functions and normal-bounded uncertainties, and give the conditions of the global robust stability of systems in terms of a linear matrix inequality. After that, based on the linear matrix inequality technology and Filippov theory, we give the sufficient conditions for the global robust stability of delayed neural networks with discontinuous activation functions and interval uncertainties. Finally, we introduce the models and applications of neural networks in robotic compensated control.
The second part mainly deals with the study of trajectory tracking robust control for nonlinear rigid robot systems. At first, we briefly tell the history of rigid robotic systems, and then, introduce in detail the research progress of trajectory tracking control problems about nonlinear rigid robot systems and the application of intelligent control theory in robotic systems. Secondly, the dynamics model and its characteristics of rigid robotic system are introduced respectively, and then, we introduce some important mathematical concepts and definitions. Thirdly, we address the problem of robust tracking control using a PD-plus-feedforward controller and an intelligent adaptive robust compensator for a rigid robotic manipulator with uncertain dynamics and external disturbances. In this way, chattering can be effectively eliminated and asymptotic error convergence can be guaranteed. After that, A novel robust H_∞intelligent control strategy is proposed for the trajectory following problem of robot manipulators. The proposed system is comprised of a computed torque controller and neural robust controller. Based on Lyapunov stability theorem, it is shown that the proposed controller can guarantee H_∞tracking performance of robotic system in the sense that all variables of the closed-loop system are bounded. Finally, the problem of the robust tracking for a class of uncertain robotic systems with delays is investigated. A neural network system is used to approximate an unknown controlled system from the strategic manipulation of the model following tracking errors. Based on the Lyapunov method and the linear matrix inequality approach, several sufficient conditions, which guarantee the robust stability of closed error systems, are derived.
The third part mainly deals with the study of trajectory tracking robust control for a kind of nonlinear nonholonomic mobile robot systems. Firstly, we introduce in detail the research progress of trajectory tracking control problems about nonlinear mobile robot systems and the application of intelligent control theory in mobile robotic systems. Secondly, the kinematics and dynamics model and its characteristics of mobile robotic system are introduced. After that, we propose a stable tracking control rule for nonholonomic mobile robot with completely unknown robot dynamics and unmodeled disturbance. A control strategy that integrate a kinematic controller and a adaptive wavelet neural network controller for nonholonomic mobile robots is presented. The adaptive wavelet neural network control system adopts a wavelet neural network with accurate approximation capability to represent the unknown dynamics of the nonholonomic mobile robot. It also uses a robust term to confront the inevitable approximation errors due to the finite number of wavelet bases functions and to disturbances. The tracking stability of the closed loop system, the convergence of the wavelet neural network weight-updating process and boundedness of wavelet neural network weight estimation errors are all guaranteed.
Finally, the main innovations of the thesis are summarized, and the fields for further research are expected.
第一部分主要研究了非线性动态神经网络系统的稳定性性质.首先,简单回顾了神经网络的发展历史以及稳定性理论的相关研究进展.其次,研究了一类带区间不确定性的不连续神经网络系统的全局鲁棒稳定性,利用Lyapunov-Krasovskii稳定性方法,首次给出了带区间不确定性的不连续型神经网络系统全局鲁棒稳定的充分条件.随后,研究了一类带范数有界不确定性的不连续神经网络系统的全局鲁棒稳定,并给出了基于线性矩阵不等式的系统全局鲁棒稳定条件.然后,通过利用线性矩阵不等式(LMI)技术和Filippov理论,给出了一类带区间不确定性的不连续神经网络系统的全局鲁棒稳定条件.最后,介绍了机器人补偿控制中的神经网络模型及其应用.
第二部分深入研究了非线性刚性机器人系统的路径跟踪鲁棒控制问题.首先,简单叙述了机器人的发展历史,详细介绍了刚性机器人系统路径跟踪问题的研究进展和智能控制理论在机器人中的应用.接着,介绍了刚性机器人的动力学模型和相关性质,并给出了研究所需的相关数学基础.然后,研究了一类刚性机器人系统的智能混合轨迹跟踪控制.通过结合PD+前馈控制器和智能鲁棒补偿器,使得刚性机器人系统具有较强的抗干扰能力和良好的鲁棒跟踪性能.其次,分析了一类刚性机器人系统智能鲁棒H_∞控制问题.控制策略基于Lyapunov稳定性理论,结合计算力矩控制器和神经网络鲁棒控制器,保证了刚性机器人系统的鲁棒H_∞跟踪性能.最后,我们分析了一类带时滞的刚性机器人系统神经网络鲁棒跟踪控制问题,利用神经网络来逼近机器人系统的未知不确定部分,使得控制系统具有较强的自适应能力和跟踪性能,并基于线性矩阵不等式技术和Lyapunov稳定性理论,得到了跟踪误差闭环系统的鲁棒稳定性条件.
第三部分针对一类非完整移动机器人系统的路径跟踪鲁棒控制问题进行了深入研究.首先,结合现代控制技术,详细介绍了非完整移动机器人系统路径跟踪问题的研究进展和智能控制理论在移动机器人中的应用.然后,介绍了移动机器人的动力学和运动学建模.接着,研究了基于小波神经网络的非完整移动机器人系统的智能鲁棒控制问题.控制策略采用了运动控制器和自适应小波神经网络控制器相结合的办法,利用小波神经网络来逼近非完整机器人系统的未知动力学部分,同时采用一个鲁棒控制器来补偿小波神经网络的逼近误差和外部干扰,设计了小波神经网络的在线学习算法,保证了权值自适应率的收敛性和跟踪误差闭环系统的鲁棒稳定性.
论文最后总结了全文的主要创新研究成果,并对下一步研究工作进行了展望.
Along with the development of science and technology, the system object or process become larger and more complex in structure and scale than ever. Therefore, it is hard to get the accurate mathematic model of the system. In this way, it is very important to research the uncertain nonlinear dynamic systems for the purpose of theory significance and practical needs. This paper mainly deals with the study of stability and robust control for several kinds of nonlinear dynamic systems. Our research work mainly boils down to the following three parts: firstly, we discuss the stability of nonlinear dynamic neural network systems, and then, we work on the problem of trajectory tracking robust control for nonlinear rigid robot systems, finally, we discuss the problem of trajectory tracking robust control for a kind of nonlinear nonholonomic mobile robot system. The content of this paper can be listed as following three parts.
The first part mainly deals with the study of stability for nonlinear dynamic neural network systems. At first, we brief introduce the history of neural networks and the research progress of stability theory, and then, we examine the global robust stability of delayed neural networks with discontinuous activation functions and interval uncertainties. Based on the Lyapunov-Krasovskii stability method, we originally give the sufficient conditions for the global robust stability of delayed neural networks with discontinuous activation functions and interval uncertainties. Secondly, we analyze the global robust stability of delayed neural networks with discontinuous activation functions and normal-bounded uncertainties, and give the conditions of the global robust stability of systems in terms of a linear matrix inequality. After that, based on the linear matrix inequality technology and Filippov theory, we give the sufficient conditions for the global robust stability of delayed neural networks with discontinuous activation functions and interval uncertainties. Finally, we introduce the models and applications of neural networks in robotic compensated control.
The second part mainly deals with the study of trajectory tracking robust control for nonlinear rigid robot systems. At first, we briefly tell the history of rigid robotic systems, and then, introduce in detail the research progress of trajectory tracking control problems about nonlinear rigid robot systems and the application of intelligent control theory in robotic systems. Secondly, the dynamics model and its characteristics of rigid robotic system are introduced respectively, and then, we introduce some important mathematical concepts and definitions. Thirdly, we address the problem of robust tracking control using a PD-plus-feedforward controller and an intelligent adaptive robust compensator for a rigid robotic manipulator with uncertain dynamics and external disturbances. In this way, chattering can be effectively eliminated and asymptotic error convergence can be guaranteed. After that, A novel robust H_∞intelligent control strategy is proposed for the trajectory following problem of robot manipulators. The proposed system is comprised of a computed torque controller and neural robust controller. Based on Lyapunov stability theorem, it is shown that the proposed controller can guarantee H_∞tracking performance of robotic system in the sense that all variables of the closed-loop system are bounded. Finally, the problem of the robust tracking for a class of uncertain robotic systems with delays is investigated. A neural network system is used to approximate an unknown controlled system from the strategic manipulation of the model following tracking errors. Based on the Lyapunov method and the linear matrix inequality approach, several sufficient conditions, which guarantee the robust stability of closed error systems, are derived.
The third part mainly deals with the study of trajectory tracking robust control for a kind of nonlinear nonholonomic mobile robot systems. Firstly, we introduce in detail the research progress of trajectory tracking control problems about nonlinear mobile robot systems and the application of intelligent control theory in mobile robotic systems. Secondly, the kinematics and dynamics model and its characteristics of mobile robotic system are introduced. After that, we propose a stable tracking control rule for nonholonomic mobile robot with completely unknown robot dynamics and unmodeled disturbance. A control strategy that integrate a kinematic controller and a adaptive wavelet neural network controller for nonholonomic mobile robots is presented. The adaptive wavelet neural network control system adopts a wavelet neural network with accurate approximation capability to represent the unknown dynamics of the nonholonomic mobile robot. It also uses a robust term to confront the inevitable approximation errors due to the finite number of wavelet bases functions and to disturbances. The tracking stability of the closed loop system, the convergence of the wavelet neural network weight-updating process and boundedness of wavelet neural network weight estimation errors are all guaranteed.
Finally, the main innovations of the thesis are summarized, and the fields for further research are expected.
引文
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