非完整控制系统的非线性控制策略研究
摘要
非完整系统来源于经典机械系统, 它的本质是存在不可积分线性约束的Lagrange系统。由于非完整控制系统为本质上的非线性系统，线性控制策略对其显得无能为力，同时光滑时变状态反馈只能使系统达到渐近收敛，无法达到全局一致指数收敛的要求。非完整控制系统控制目标可以分为运行规划、镇定和跟踪控制，本文重点研究了非完整控制系统的镇定和跟踪控制两个问题。
非完整控制系统作为一个综合性的控制系统广泛存在于现实世界当中，该课题在当前研究具有重要的理论和实际意义。本文完成了如下几方面的工作：
对非完整控制系统进行了综述，分析了非完整系统的模型和一些基本的定义、定理，并对当前非完整控制系统存在的难点和问题进行了论述。
对于三维非完整控制系统，由于非完整双积分模型和感应电动机的模型之间存在一定的等价关系，本文把电动机中常用的矢量控制方法运用在非完整系统的控制中，实现了系统的全局镇定和跟踪控制。
为了解决非完整控制系统的高维控制问题，本文把微分几何中的不变流形控制方法运用于非完整控制系统的镇定控制中，由于不变流形在处理高维控制问题有其独到的优点，因此不变流形在非完整控制系统的应用具有开拓性的意义。
非完整控制系统的状态观测问题对于非完整控制设计具有重要的意义，非完整控制系统的输出反馈控制问题是一个很有挑战性的课题，文中采用基于观测器的动态输出反馈控制实现了非完整控制系统的全局k-指数渐近跟踪。
针对确定非完整链式系统设计了变结构控制器，并分析了其鲁棒性能；由于变结构控制的设计要求系统的全部状态已知，文中又给出了基于观测器的滑模变结构控制设计方案，实现了非完整控制系统的全局指数镇定控制。
针对不确定非完整链式系统，本文设计了鲁棒Backstepping 控制器来解决其不确定性问题，并对于一定的不确定性分析了其鲁棒性能。
Nonholonomic systems originate from classical mechanics systems. Its essence is Lagrange system with linear constraints being nonintegrable. Since nonholonomic control systems are nonlinear systems in essence, linear control strategies haven’t the ability to solve the control problems of nonholonomics control systems. Smooth time-variant state feedback can only make the system asymptotically stabilized, which can’t make the system globally exponentially stabilized. The goal of nonholonomic control systems can be divided as motion planning, stabilization and tracking control. In this paper, we emphasize the research on the stabilization and tracking control of nonholonomic control systems.
Nonholonomic control systems are comprehensive control systems which widely exist in the real world. The researches in this field have their theory and practice meanings. In this paper, we have accomplished the following researches:
Nonholonomic control systems are summarized firstly. Some mathematics models, definitions and theorems are analyzed. And some difficulties and problems of nonholonomic control systems are also given.
Nonholonomic double integrator model is equivalence to induction motor model in the case of simple three-dimension nonholonomic control systems. We apply field-oriented control model of motor to nonholonomic control systems and realize global exponential stabilization and tracking control.
Invariant manifold of differential geometry is applied to stabilization of nonholonomic control systems to solve the high dimension control problems. Since invariant manifold has its original excellence to deal with high dimension problems, invariant manifold has its special significance in the control of nonholonomic control systems.
State observation problem has its significance in the control of nonholonomic control systems. Output feedback control problem is a challenge topic of nonholonomic control systems. Dynamic output feedback control based on observer is applied to realize globally k-exponentially gradually tracking control.
Variable structure control is applied to nonholonomic chained system and its robust performance is analyzed. Since variable structure control need all the system states to be known, variable structure control based on observer is designed to realize
globally exponentially stabilization of nonholonomic control system.
Robust backstepping control is applied to uncertain nonholonomic chained system to solve its uncertainty problem and its robust performance is analyzed to some uncertainty.
非完整控制系统作为一个综合性的控制系统广泛存在于现实世界当中，该课题在当前研究具有重要的理论和实际意义。本文完成了如下几方面的工作：
对非完整控制系统进行了综述，分析了非完整系统的模型和一些基本的定义、定理，并对当前非完整控制系统存在的难点和问题进行了论述。
对于三维非完整控制系统，由于非完整双积分模型和感应电动机的模型之间存在一定的等价关系，本文把电动机中常用的矢量控制方法运用在非完整系统的控制中，实现了系统的全局镇定和跟踪控制。
为了解决非完整控制系统的高维控制问题，本文把微分几何中的不变流形控制方法运用于非完整控制系统的镇定控制中，由于不变流形在处理高维控制问题有其独到的优点，因此不变流形在非完整控制系统的应用具有开拓性的意义。
非完整控制系统的状态观测问题对于非完整控制设计具有重要的意义，非完整控制系统的输出反馈控制问题是一个很有挑战性的课题，文中采用基于观测器的动态输出反馈控制实现了非完整控制系统的全局k-指数渐近跟踪。
针对确定非完整链式系统设计了变结构控制器，并分析了其鲁棒性能；由于变结构控制的设计要求系统的全部状态已知，文中又给出了基于观测器的滑模变结构控制设计方案，实现了非完整控制系统的全局指数镇定控制。
针对不确定非完整链式系统，本文设计了鲁棒Backstepping 控制器来解决其不确定性问题，并对于一定的不确定性分析了其鲁棒性能。
Nonholonomic systems originate from classical mechanics systems. Its essence is Lagrange system with linear constraints being nonintegrable. Since nonholonomic control systems are nonlinear systems in essence, linear control strategies haven’t the ability to solve the control problems of nonholonomics control systems. Smooth time-variant state feedback can only make the system asymptotically stabilized, which can’t make the system globally exponentially stabilized. The goal of nonholonomic control systems can be divided as motion planning, stabilization and tracking control. In this paper, we emphasize the research on the stabilization and tracking control of nonholonomic control systems.
Nonholonomic control systems are comprehensive control systems which widely exist in the real world. The researches in this field have their theory and practice meanings. In this paper, we have accomplished the following researches:
Nonholonomic control systems are summarized firstly. Some mathematics models, definitions and theorems are analyzed. And some difficulties and problems of nonholonomic control systems are also given.
Nonholonomic double integrator model is equivalence to induction motor model in the case of simple three-dimension nonholonomic control systems. We apply field-oriented control model of motor to nonholonomic control systems and realize global exponential stabilization and tracking control.
Invariant manifold of differential geometry is applied to stabilization of nonholonomic control systems to solve the high dimension control problems. Since invariant manifold has its original excellence to deal with high dimension problems, invariant manifold has its special significance in the control of nonholonomic control systems.
State observation problem has its significance in the control of nonholonomic control systems. Output feedback control problem is a challenge topic of nonholonomic control systems. Dynamic output feedback control based on observer is applied to realize globally k-exponentially gradually tracking control.
Variable structure control is applied to nonholonomic chained system and its robust performance is analyzed. Since variable structure control need all the system states to be known, variable structure control based on observer is designed to realize
globally exponentially stabilization of nonholonomic control system.
Robust backstepping control is applied to uncertain nonholonomic chained system to solve its uncertainty problem and its robust performance is analyzed to some uncertainty.
引文
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