分布时滞中立系统的鲁棒滤波方法研究

发布时间：2019-05-25 02:45

【摘要】：在各种实际工程系统中,时滞现象大量存在,如信号处理、网络控制系统、皮带传输等。时滞的出现常常致使系统不稳定和系统性能变差。同时,也加大了系统分析与综合问题的难度。因此,分析时滞对系统的影响,并利用或减小这种影响一直是人们关注的热点问题。近年来,作为时滞系统的重要领域,中立时滞系统因其可以同时描述系统状态滞后和状态微商滞后而受到广泛研究。分布时滞普遍出现在系统方程中求和数量剧增且相邻决定值之间差异变小的情况,如火箭发动机的流体火药燃烧过程建模和材料热加工等考虑不均匀延迟的系统。客观上看,分布时滞能够更精确的描述系统,揭示事物变化的本质。因此研究分布时滞中立系统具有重要的实际意义。此外,考虑由于数学建模误差、条件变化及外界干扰等引起的不确定性对系统的影响也是必不可少的。本文主要研究了含有分布时滞的不确定中立系统的鲁棒滤波问题,并通过实例仿真证明了文中所提的方法是切实可行且有效的。首先,针对一类具有混合时滞的不确定中立时滞系统,设计其鲁棒H?和2L L?-滤波器。混合时滞包含离散时滞和分布时滞,并同时存在于状态方程和输出方程中。系统中的参数不确定性被假设为时变且范数有界的。通过构造适当的Lyapunov函数,结合积分不等式技术,建立了满足相应性能指标的滤波器存在的时滞依赖条件,保证滤波误差系统渐近稳定。根据所得到的规则,采用变量替换法,以线性矩阵不等式的形式给出滤波器的设计方法。仿真例子检验了所提方法的可行性。其次,针对具有Markov跳变参数的不确定分布时滞中立系统,研究其鲁棒H?和2L L?-滤波器的设计问题。通过建立模态依赖的Lyapunov函数,利用伊藤微分和牛顿-莱布尼兹公式,提出了使滤波误差系统随机稳定且满足给定性能指标的滤波器存在的充分条件。利用矩阵变换等方法实现Lyapunov函数矩阵和系统矩阵之间的解耦,再经过求解线性矩阵不等式的凸优化问题,得到滤波器的参数。仿真算例表明设计方法的低保守性。最后,研究了非线性无穷分布时滞中立系统的鲁棒H?和2L L?-滤波问题。系统中的非线性受到Lipschitz条件的约束,依据Lyapunov函数方法,引入柯西不等式处理无穷分布时滞项,充分考虑时滞相关的信息,利用积分不等式等方法,将非线性条件转换成线性条件,给出了更易于求解的滤波器的设计方法。对于所容许的不确定性和所有能量有界的外界干扰,所设计的滤波器不仅能够确保滤波误差系统是渐近稳定的,同时满足相应的扰动衰减水平。数值仿真验证了所设计的滤波器能够很好的还原原系统状态,减小了未知干扰的影响。
[Abstract]:In various practical engineering systems, there are a large number of time delay phenomena, such as signal processing, network control system, belt transmission and so on. The emergence of time delay often leads to system instability and system performance. At the same time, it also increases the difficulty of system analysis and synthesis. Therefore, it has been a hot issue to analyze the influence of time delay on the system and to make use of or reduce it. In recent years, as an important field of time-delay systems, neutral time-delay systems have been widely studied because they can describe the state delay and state derivative delay of the system at the same time. The distributed time delay generally occurs in the system equation when the summation quantity increases sharply and the difference between adjacent determining values becomes smaller, such as the modeling of fluid gunpowder combustion process of rocket engine and the thermal processing of materials. Objectively speaking, distributed time delay can describe the system more accurately and reveal the nature of the change of things. Therefore, it is of great practical significance to study the distributed delay neutral system. In addition, it is necessary to consider the uncertainty caused by mathematical modeling error, condition change and external interference. In this paper, the robust filtering problem for uncertain neutral systems with distributed delays is studied, and the simulation results show that the proposed method is feasible and effective. First of all, for a class of uncertain neutral time-delay systems with mixed delays, a robust H-H is designed for a class of uncertain neutral time-delay systems with mixed delays. And 2L / L / L filter. Mixed delays include discrete delays and distributed delays, and exist in both the equation of state and the output equation. The parameter uncertainty in the system is assumed to be time-varying and norm-bounded. By constructing the appropriate Lyapunov function and combining with the integral inequality technique, the delay dependent condition of the filter satisfying the corresponding performance index is established to ensure the asymptotic stability of the filtering error system. According to the obtained rules, the variable substitution method is used to give the design method of the filter in the form of linear matrix inequality (LMI). A simulation example is given to verify the feasibility of the proposed method. Secondly, the robust H? for uncertain distributed delay neutral systems with Markov jump parameters is studied. And the design of 2L / L / L filter. By establishing the modal dependent Lyapunov function and using Ito differential and Newton-Leibniz formula, a sufficient condition for the existence of the filter whose filtering error system is randomly stable and satisfies the given performance index is put forward. The decoupling between Lyapunov function matrix and system matrix is realized by matrix transformation, and then the convex optimization problem of linear matrix inequality is solved, and the parameters of filter are obtained. Simulation examples show the low conservatism of the design method. Finally, the robust H? And 2L / L / L filtering problem. The nonlinear in the system is constrained by the Lipschitz condition. According to the Lyapunov function method, Cauchy inequality is introduced to deal with the infinite distributed delay term, the delay related information is fully considered, and the integral inequality is used. The nonlinear condition is transformed into linear condition, and the design method of filter which is easier to solve is given. For the allowable uncertainty and all energy-bounded external interference, the designed filter can not only ensure that the filtering error system is asymptotically stable, but also satisfy the corresponding disturbance attenuation level. The numerical simulation results show that the designed filter can reduce the state of the original system and reduce the influence of unknown interference.
【学位授予单位】：东北石油大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TN713

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