几类高阶非线性系统的稳定分析与控制问题研究

发布时间：2018-07-03 02:36

本文选题：非线性系统 + 随机系统　；参考：《曲阜师范大学》2016年博士论文

【摘要】：在实际系统中,非线性、时滞、外部随机干扰等是普遍存在的.近几年,一类高阶非线性系统的控制设计问题得到了广泛的研究,尤其对其有限时间的镇定问题更成为目前的研究热点.本文针对几类不同结构的高阶非线性(随机)系统,研究了它们的控制器设计和稳定性分析问题.主要研究成果包括:1.针对一类具有高、低阶次非线性项的高阶非线性系统,研究了全局渐近输出反馈镇定问题.主要解决了以下问题:(i)非线性项不仅同时具有高阶次和低阶次,并且高、低阶次同时被放宽到区间任意实数.(ii)由于非线性项中高、低阶次的一般性,符号函数被引入到控制器设计当中.(iii)基于增加幂次积分,齐次占优法和Lypunov稳定性定理,系统的输出反馈镇定控制器被设计并且保证了闭环系统平衡点全局渐近稳定性.2.对一类高阶多时变时滞非线性系统,研究了它的状态反馈渐近镇定问题.系统非线性项高、低阶次的同时出现及其形式的一般,再加上多时变时滞的出现使得系统更具一般性.通过引入新的Lyapunov-Krasovskii(L-K)泛函,结合运用增加幂次积分法和符号函数,设计了一个全局状态反馈渐近镇定控制器.3.针对一类具有高、低阶次非线性项的高阶非线性下三角系统,基于有限时间Lyapunov稳定性定理,结合动态增益法和增加幂次积分法,设计了一个具有动态增益的全局有限时间镇定控制器.4.针对一类高阶非线性上三角系统,研究了它的有限时间输出反馈镇定问题.根据齐次占优法,在一组坐标变换下,首先为标称系统设计一个输出反馈控制器.然后通过构造一个降阶观测器并确定观测增益来得到完整系统的一个有限时间输出反馈控制器.最后,通过分析和仿真举例验证了有限时间输出反馈镇定控制器设计方案的有效性.5.研究了具有更弱非线性假设条件的高阶随机非线性系统的依概率有限时间镇定问题.主要有两方面的难点:(i)去掉了系统非线性项的上界必须具有线性项的限制.(ii)理论分析了解的存在唯一性这一研究前提.6.研究了高阶随机非线性前馈系统的依概率有限时间镇定问题.基于随机Lyapunov有限时间稳定性定理和齐次占优法,通过构造了一个2 Lyapunov函数以及验证解的存在唯一性,设计了一个连续依概率有限时间镇定控制器.最后的仿真实例验证了设计方案的有效性.7.研究了高阶随机非线性前馈系统的依概率有限时间输出反馈镇定问题.基于随机Lyapunov有限时间稳定性定理和齐次占优法,通过构造了一个降阶随机观测器以及验证解的存在唯一性,设计并分析了一个依概率有限时间输出反馈镇定控制器.
[Abstract]:In practical systems, nonlinearity, time delay and external random disturbances are common. In recent years, the control design problem of a class of high order nonlinear systems has been widely studied, especially the stabilization of its finite time has become a hot research topic. In this paper, the controller design and stability analysis of several kinds of high order nonlinear (stochastic) systems with different structures are studied. The main research results include: 1. The global asymptotically output feedback stabilization problem is studied for a class of high order nonlinear systems with high and low order subnonlinear terms. The following problems are solved: the (i) nonlinear term not only has high order and low order, but also high and low order, and is extended to the generality of high and low order. (ii) because of the nonlinear term. The sign function is introduced into the controller design based on the addition of power integral, homogeneous dominant method and Lyapunov stability theorem. The output feedback stabilization controller of the system is designed and guaranteed the global asymptotic stability of the closed-loop system equilibrium point. The problem of state feedback asymptotic stabilization for a class of high order nonlinear systems with multiple time-varying delays is studied. The system is more general because of its high nonlinear term, low order simultaneous occurrence and its form, plus the appearance of multiple time-varying delays. By introducing a new Lyapunov-Krasovskii (L-K) functional, a global state feedback asymptotic stabilization controller. For a class of high order nonlinear lower triangular systems with high and low order nonlinear terms, based on the Lyapunov stability theorem of finite time, the dynamic gain method and the power adding integral method are combined. A global finite time stabilization controller .4. with dynamic gain is designed. For a class of high order nonlinear upper triangular systems, the finite time output feedback stabilization problem is studied. According to the homogeneous dominant method, an output feedback controller is designed for the nominal system under a set of coordinate transformations. Then a finite time output feedback controller for the complete system is obtained by constructing a reduced order observer and determining the observation gain. Finally, the effectiveness of the design scheme of finite time output feedback stabilization controller is verified by an analysis and simulation example. In this paper, the problem of time-dependent stabilization for higher order stochastic nonlinear systems with weaker nonlinear assumptions is studied. There are two main difficulties: (i) removed the upper bound of the nonlinear term of the system must have the limit of the linear term of the existence and uniqueness of the. (ii) theoretical analysis solution. 6. The probabilistic finite time stabilization problem for high order stochastic nonlinear feedforward systems is studied. Based on the stochastic Lyapunov finite time stability theorem and homogeneous dominant method, a continuous time-dependent finite time stabilization controller is designed by constructing a 2Lyapunov function and verifying the existence and uniqueness of the solution. Finally, a simulation example is given to verify the effectiveness of the design. 7. The problem of output feedback stabilization based on probability finite time for high order stochastic nonlinear feedforward systems is studied. Based on the stochastic Lyapunov finite time stability theorem and homogeneous dominant method, a reduced order stochastic observer is constructed and the existence and uniqueness of the solution is verified. A feedback stabilization controller based on probability finite time output is designed and analyzed.
【学位授予单位】：曲阜师范大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TP13

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