【作者】 孙宗耀；

【导师】 刘允刚；

【作者基本信息】 山东大学 ， 控制理论与控制工程， 2009， 博士

【摘要】 近几年来,一类所谓的高阶非线性系统的控制设计问题倍受科研工作者关注.从系统模型上来看,高阶非线性系统是已经得到大量研究的严格反馈非线性系统的更一般形式.另一方面,高阶非线性系统包含实际中一类很难控制的欠驱动、弱耦合和不稳定的机械系统.因此,它们的控制问题的研究有重要的理论意义和一定的实际意义.但是,高阶系统的控制问题不能用传统的反馈线性化方法或者反推方法进行解决.本文主要研究了高阶不确定非线性系统的控制设计问题.针对几类不同的高阶不确定非线性系统,利用增加幂次积分方法、反推方法、灵活的自适应技术和其他一些处理技巧(如Young不等式等),分别设计了光滑的状态反馈全局自适应镇定控制器、连续的状态反馈全局自适应镇定控制器、连续的自适应实际输出跟踪控制器和光滑的自适应输出反馈镇定控制器,并给出了这几类控制器的具体的设计步骤.此外,借助于常微分方程解的存在唯一性理论、Lyapunov稳定性理论和Barbalat引理,分析了所设计的白适应控制器的性能.本文的主要内容分为以下四个部分:一、一类高阶不确定非线性系统的自适应状态反馈镇定本部分研究了一类高阶不确定非线性系统的状态反馈全局自适应镇定问题.在未知控制系数的下界精确已知的假设条件下,这一问题已经得到了较为广泛的研究.本部分去除了这一假设条件,并系统地推导出了一类有未知控制系数的高阶不确定非线性系统的自适应镇定控制器构造的统一化方法.利用所谓的增加幂次积分方法和自适应技术,给出了光滑自适应状态反馈控制器的迭代设计步骤,所设计的控制器确保整个闭环系统是全局一致稳定的,同时确保原系统的状态全局渐近收敛到零.最后,给出了一个仿真算例来验证理论结果的正确性.二、一类更广泛的高阶不确定非线性系统的自适应状态反馈镇定本部分研究了一类有未知控制系数和零动态的高阶不确定非线性系统的状态反馈全局自适应镇定问题.首先,引入了某些恰当的未知参数,以获得在自适应控制设计中的修正律.然后,灵活结合增加幂次积分方法、自适应技术和交换能量函数的思想,放宽了对不确定控制系数的假设条件,并成功地推导出了连续自适应镇定控制器的迭代设计步骤.所设计的控制器确保整个闭环系统的所有状态是全局一致有界的,同时确保原系统的状态全局渐近收敛到零.最后.给出了一个例子来验证理论结果的正确性.三、一类高阶不确定非线性系统的自适应实际输出跟踪控制本部分研究了一类高阶不确定非线性系统的自适应实际输出跟踪控制问题,该问题在未知的控制系数的下界精确已知的假设下已经得到了研究.基于新的鲁棒自适应控制和连续镇定的思想,成功地去除了控制系数下界精确已知的假设条件.借助于增加幂次积分方法,推导出了构造连续的自适应实际输出跟踪控制器的系统化的方法,该控制器确保闭环系统的所有状态是全局稳定的,同时,在经过某一有限的时刻后,跟踪误差可以小于事先给定的任意正数.最后,给出了一个仿真算例来验证理论结果的正确性.四、一类二维高阶不确定非线性系统的自适应输出反馈镇定本部分研究了一类不确定非线性系统输出反馈镇定问题.首先构造了合适的状态观测器,进而基于增加幂次积分方法和自适应技术,给出了设计光滑自适应输出反馈控制器的新方法.主要理论结果表明:所设计的控制器不仅保证闭环系统的所有状态均是有界的,而且原系统的状态和观测器的状态渐近收敛到零.总之,高阶不确定非线性系统控制问题的圆满解决不仅会对严格反馈非线性控制系统的理论研究起着指导作用,另一方面也将丰富传统的控制器的设计方法.更多还原

【Abstract】 The problems of the control design for a class of so-called high-order nonlinear systems have been widely studied by researchers in recent years. From the view point of the system model, high-order nonlinear systems represent a more general form of strict feedback nonlinear systems that have been extensively investigated. On the other hand, high-order nonlinear systems include a class of under-actuated, weakly coupled and unstable mechanical systems which are exceptionally difficult to dominate in practice. Therefore, the investigations of control problems for high-order systems have theoretical and practical meanings. However, the control problems can not be solved by the traditional feedback linearization method or backstepping approach.The dissertation focuses on the investigation of the control design for high-order uncertain nonlinear systems. For several different classes of high-order uncertain nonlinear systems, in virtue of the method of adding a power integrator, flexible adaptive technique and other techniques such as Young’s inequality, a smooth state-feedback global adaptive stabilizing controller, a continuous state-feedback global adaptive stabilizing controller, a continuous adaptive practical output tracking controller and a smooth adaptive output feedback stabilizing controller are designed respectively, and detailed design procedures of controllers are provided. In addition, by means of existence and uniqueness theorem for ordinary differential equations, Lyapunov stabilization theorem and Barbalat lemma, the corresponding performance analyses of adaptive controllers designed are given. The main contents of this paper are composed of the following four parts:(Ⅰ) Adaptive state-feedback stabilization for a class of high-order uncertain nonlinear systemsThis part studies the problem of global adaptive stabilization by state-feedback for a class of high-order nonlinear systems with unknown control coefficients. For the control design of this class of systems, there have been a lot of investigations under a strong assumption that the lower bounds of the unknown control coefficients should be exactly known. In this part, this assumption is removed and a unified approach is developed to systematically construct a state-feedback adaptive stabilizing controller for a class of high-order uncertain nonlinear systems with unknown control coefficients. By using the method of the so-called adding a power integrator merging with adaptive technique, a recursive design procedure is provided to achieve a smooth adaptive state-feedback controller, which guarantees that the whole closed-loop system is globally uniformly stable, while the original system states globally asymptotically converge to zero. Finally, a simulation example is given to illustrate the correctness of the theoretical results.(Ⅱ) Adaptive state-feedback stabilization for a large class of high-order uncertain nonlinear systemsThis part investigates the problem of global adaptive stabilization by state-feedback for a class of high-order nonlinear systems with unknown control coefficients and zero dynamics. First, some appropriate unknown parameters are introduced to obtain the updating laws when adapting control design. Then, by the flexible way of combining adding a power integrator with adaptive technique and the idea of changing supply functions, the requirement on the unknown control coefficients is relaxed, and a recursive design procedure is successfully developed to achieve a continuous adaptive stabilizing controller. The controller designed guarantees that all the states of the whole closed-loop system are globally uniformly bounded, while the original system states globally asymptotically converge to zero. Finally, an example is provided to illustrate the correctness of the theoretical results.(Ⅲ) Adaptive practical output tracking control for a class of high-order uncertain nonlinear systemsThis part studies the problem of adaptive practical output tracking control for a class of high-order uncertain nonlinear systems, which has been investigated under the assumption that the lower bounds of the unknown control coefficients are exactly known. Based on the idea of the new robust adaptive control and the continuous stabilization, this assumption is successfully removed. By means of adding a power integrator, a systematic approach is developed to construct a continuous adaptive practical output tracking controller, which guarantees that all the states of the closed-loop system are globally stable, while the tracking error can be bounded by any given positive number after a finite time. Finally, a simulation example is given to illustrate the correctness of the theoretical results.(Ⅳ) Adaptive output feedback stabilization for a class of second-dimensional high-order uncertain nonlinear systemsThis part investigates the stabilizing problem for a class of uncertain nonlinear systems. First, an appropriate observer is introduced, and then based on adding a power integrator and adaptive technique, a new method is presented to construct a smooth adaptive output feedback controller. The main theoretical results show that the controller designed not only guarantees that all the states of the closed-loop systems are bounded, but also the states of the original system and the observer converge to zero asymptotically.All in all, satisfactory solutions to control problems of high-order uncertain nonlinear systems not only guide the academic research of strict feedback nonlinear control systems, but also will enrich the design methods of traditional controllers.更多还原