几类非线性随机系统的稳定分析与控制

发布时间：2018-05-02 16:51

本文选题：随机系统 + LaSalle定理　；参考：《南京理工大学》2016年博士论文

【摘要】：作为非线性系统的重要组成部分,非线性随机系统因考虑了多种多样的环境噪声,已被广泛应用到电力系统、通信系统等实际工程领域,并且在这些领域中发挥出了十分重要的作用.此外,由于随机干扰的复杂性,使得对随机系统的分析与控制比确定性情形更加困难、更加复杂.因此,研究非线性随机系统的稳定性分析与控制器设计是一项具有非常重要的理论意义和实际应用价值的研究课题.本文针对几类重要的非线性随机系统,基于时变控制方法、自适应控制方法、随机LaSalle定理、随机Lyapunov-Krasovskii泛函稳定理论和多Lyapunov函数技术等理论方法,深入研究了反馈控制器设计以及稳定性分析问题,提出了有效的控制策略,获得了新的稳定性判定条件.本文的主要研究工作包括:1.针对一类具有未知增长速率的随机上三角系统,研究了基于时变控制方法的状态反馈控制问题.首先,通过引入广义弱正定函数,给出LaSalle定理的推广形式.其次,采取时变方法而非自适应技术抑制了不确定增长速率的影响,并结合Backstepping技术给出了状态反馈控制器设计方法.最后,利用LaSalle定理,证明了闭环系统具有全局唯一解并且解过程几乎必然收敛到零.2.针对一类大规模随机高阶上三角时滞系统,研究了分散状态反馈控制问题.结合Backstepping方法和增加幂次积分技术,设计了分散无记忆状态反馈控制器.利用Lyapunov-Krasovskii稳定性理论,证明了闭环系统的随机全局渐近稳定性.提供的仿真算例验证了设计方法的有效性.3.针对一类大规模非线性随机时滞系统,研究了分散自适应输出反馈控制问题.首先设计滤波器以估计不可测状态,在此基础上通过使用Backstepping技术,逐步设计出无记忆的虚拟控制信号和实际控制器.通过引入四次Lyapunov函数,利用LaSalle定理证明了闭环系统的所有信号几乎必然有界并且系统状态几乎必然收敛到零.提供的仿真算例验证了设计方法的有效性.4.研究了带有随机脉冲的非线性随机系统的噪声输入状态稳定和全局渐近稳定性.所考虑的随机噪声具有有限的二阶矩,并且随机脉冲是由一列随机变量决定的脉冲浮动.首先,给出了保证系统具有全局唯一解的一般判定条件.基于此,当连续动态是稳定的而脉冲序列消稳时,利用平均脉冲区间方法,提出了此类系统的噪声输入状态稳定和全局渐近稳定的判据.然后,当连续动态是不稳定的而脉冲序列起镇定作用时,利用逆平均脉冲区间方法,给出了使得系统噪声输入状态稳定和全局渐近稳定的充分条件.最后,通过仿真算例验证了以上理论.5.研究了具有二阶矩随机过程的切换随机系统的稳定性问题.首先,建立了系统具有全局唯一解的充分条件.其次,针对一类随机切换信号,考虑了系统的噪声输入状态稳定性.然后,采用平均驻留时间方法研究了系统的噪声输入状态稳定和全局渐近稳定.关于解的存在性以及系统的稳定性判定法则均以多Lyapunov函数的形式给出.最后,提供的仿真算例验证了理论结果的正确性.6.研究了具有二阶矩随机过程的随机马尔科夫跳变系统的稳定性及跟踪控制问题.与已有的文献不同,随机马尔科夫跳变系统的解的存在与唯一性并未作为先验信息给出,而是通过一般条件保证其成立.然后,利用Lyapunov函数方法研究了系统的噪声输入状态稳定性以及解的有界性.最后,借助得到的结论研究了输出跟踪问题,给出了状态反馈跟踪控制器的设计过程,证明了输出信号能够渐近跟踪给定的参考信号,并通过仿真结果验证了所提设计方法的有效性.
[Abstract]:As an important part of nonlinear systems, nonlinear stochastic systems have been widely used in practical engineering fields, such as power systems, communication systems, and other practical engineering fields, because of their consideration of various environmental noises. In addition, the analysis of random systems is made due to the complexity of random interference. It is more difficult and more complex than control. Therefore, the study of stability analysis and controller design for nonlinear stochastic systems is a research subject with very important theoretical significance and practical application value. This paper is based on several kinds of important nonlinear stochastic systems, based on time-varying control method and adaptive control method. The stochastic LaSalle theorem, the stochastic Lyapunov-Krasovskii functional stability theory and the multi Lyapunov function technique are used to study the design of the feedback controller and the stability analysis. The effective control strategy is proposed and the new stability criteria are obtained. The main research work of this paper includes 1. for a class of unknown variables. The problem of state feedback control based on time-varying control method is studied. First, by introducing generalized weak positive definite function, the generalized form of LaSalle theorem is given. Secondly, the effect of time-varying method and non adaptive technology is taken to restrain the influence of uncertain growth rate, and the form of Backstepping is given. In the end, using the LaSalle theorem, it is proved that the closed loop system has a global unique solution and the solution process is almost bound to converge to zero.2. for a class of large-scale random high order upper triangular time-delay systems. The decentralized state feedback control problem is studied. Combined with the Backstepping method and the power integration technique, the design is designed. The decentralized feedback controller is distributed. Using the Lyapunov-Krasovskii stability theory, the stochastic global asymptotic stability of the closed loop system is proved. The simulation example shows that the effectiveness of the design method.3. is used to study the decentralized adaptive output feedback control problem for a class of large-scale nonlinear stochastic time-delay systems. First, the design of the decentralized adaptive output feedback control problem is designed. The filter is used to estimate the unmeasurable state, and on this basis, by using the Backstepping technology, the memory free virtual control signal and the actual controller are gradually designed. By introducing the four Lyapunov functions, the LaSalle theorem is used to prove that all the signals of the closed loop system are almost bound and the state of the system almost inevitably converges to zero. The simulation example verifies the effectiveness of the design method.4. to study the stability and global asymptotic stability of the noise input state of a nonlinear stochastic system with random pulses. The random noise considered has a finite two order moment, and the random pulse is a pulse floating by a random variable. First, the guarantee system is given. Based on this, a criterion for the stability and global asymptotic stability of the noise input state of this kind of system is proposed by means of the mean pulse interval method when the continuous dynamic is stable and the pulse sequence is stable. Then, when the continuous dynamic is unstable and the pulse sequence plays a stabilizing effect, the inverse mean is used. The sufficient conditions for the stability of the system noise input state and the global asymptotic stability are given by the pulse interval method. Finally, the stability problem of the switched random system with two order moment random processes is studied by the simulation example. First, the sufficient conditions for the system with a global unique solution are established. Secondly, the problem is given. The stability of the system noise input state is considered for a class of random switching signals. Then, the state stability and global asymptotic stability of the noise input state are studied by means of the mean standing time method. The existence of the solution and the stability determination rule of the system are given in the form of multiple Lyapunov functions. Finally, the simulation example is provided. The correctness of the theoretical results.6. is given to study the stability and tracking control of a stochastic Markoff jump system with two order moment random processes. Unlike the existing literature, the existence and uniqueness of the solution of the stochastic Markoff jump system are not given as a priori information, but are guaranteed by the general conditions. The Lyapunov function method is used to study the stability of the noise input state and the boundedness of the solution. Finally, the output tracking problem is studied with the help of the obtained conclusion. The design process of the state feedback tracking controller is given. It is proved that the output signal can asymptotically track the given reference signal, and the simulation results verify the proposed design. The effectiveness of the method is calculated.

【学位授予单位】：南京理工大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O211.6;O231

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