跳变时滞不确定系统的鲁棒控制与滤波
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摘要
由于实际系统中不可避免的存在参数变化,所以对不确定系统的鲁棒控制的研究不但有理论意义,而且有很重要的应用价值。另一方面,状态估计问题在系统与控制理论、信号处理与信息融合中有很重要的应用。特别著名的估计方法是Kalman滤波方法。在Kalman滤波中,一个平常的特性是模型必须精确。可是,在很多的工业应用中,系统中含有不确定参数,精确的系统模型是很难获得的。因此,研究在模型存在不确定性下的滤波算法具有很重要的理论意义,为了克服这个困难,鲁棒滤波方法被引入。
本文基于Lyapunov稳定性理论,利用线性矩阵不等式方法分别对跳变时滞系统,中立型跳变时滞系统与广义跳变时滞系统的鲁棒控制与滤波进行了研究。所研究的系统中含有Markov跳跃参数,不确定性。跳跃参数可以用一个有限状态的Markov过程来描述。系统中的不确定是范数有界的结构不确定性。这类系统是一类混合系统,由两部分构成,第一部分是系统的模式,第二部分是系统的状态,模式可以用连续时间离散状态的Markov过程来描述,在每一个模式中,状态可由一个随机微分方程表示。本文的主要内容包括如下几个方面:
1)针对含有Markov跳跃参数的线性不确定时滞系统研究了鲁棒保性能控制,鲁棒无源控制与鲁棒耗散控制问题。目标是设计控制器,使得对容许的不确定性,闭环系统是鲁棒稳定,并且满足所提的保性能指标,无源指标与耗散指标。基于Lyapunov稳定性理论给出了相应控制器的存在条件。进一步,将控制器的设计问题转化为LMI的求解问题。通过MATLAB中线性矩阵不等式工具箱可以很容易求得相应控制器的增益矩阵。
2)基于Lyapunov稳定性理论,将含有Markov跳跃参数的线性不确定时滞系统的鲁棒控制结果推广到含有Markov跳跃参数的中立型系统中。分别对鲁棒保性能控制,鲁棒无源控制与鲁棒耗散控制问题进行了研究。目标是设计控制器,使得闭环系统鲁棒稳定,并且分别满足所提的保性能指标,无源指标与耗散指标。通过对一组关联LMI的求解,获得了相应控制器的增益矩阵。
3)将含有Markov跳跃参数的线性不确定时滞系统的鲁棒控制结果推广到含有Markov跳跃参数的广义不确定时滞系统中。分别对鲁棒保性能控制,鲁棒H∞控制,鲁棒无源控制与鲁棒耗散控制问题进行了研究。目标是设计控制器,使得对容许的不确定性,闭环系统正则,无脉冲,且鲁棒稳定,并且分别满足
Because parameter varying is inevitable in practical systems, robust control for uncertain systems is not only significant for theory research but also valuable in practice. On the other hand, state estimation plays an important role in systems and control theory, signal processing and information fusion. Certainly, the most widely used estimation method is the well-known Kalman filtering. A common feature in the Kalman filtering is that an accurate model is available. In some applications, however, when the system is subject to parameter uncertainties, the accurate system model is difficult to be obtained. To overcome this difficulty, robust filtering approaches are proposed.
This dissertation mainly considers robust and filtering for time-delay systems with Markovian jumping parameters, neutral systems with Markovian jumping parameters and descriptor time-delay systems with Markovian jumping parameters based on Lyapunov stability theory. The proposed systems contain jumping parameters and uncertainties. The transition of jumping parameters in systems is governed by a finite-state Markov process. The class of systems is a hybrid class of systems with two components in the vector state. The first component refers to the mode and the second one to the state. The mode is described by a continuous Markov process with finite state space. The state in each mode is denoted by a stochastic differential equation. The main research results in this dissertation can be given as the following.
1) Robust guaranteed cost control, passive control, dissipative control for time-delay systems with Markovian jumping parameters are proposed. The objective is to design controllers such that for all uncertainties, the resulting closed system is robust stable and satisfies the proposed guaranteed cost, passive and dissipative performance, respectively. Based on Lyapunov stability theory, sufficient conditions on the existence of robust controllers are derived, respectively. Controllers are designed in terms of linear matrix inequalities. By using LMI toolbox in MATLAB, it is easily to obtain controllers gain matrices.
2) Based on Lyapunov stability theory, the results on robust control for time-delay systems with Markovian jumping parameters are extended to neutral
本文基于Lyapunov稳定性理论,利用线性矩阵不等式方法分别对跳变时滞系统,中立型跳变时滞系统与广义跳变时滞系统的鲁棒控制与滤波进行了研究。所研究的系统中含有Markov跳跃参数,不确定性。跳跃参数可以用一个有限状态的Markov过程来描述。系统中的不确定是范数有界的结构不确定性。这类系统是一类混合系统,由两部分构成,第一部分是系统的模式,第二部分是系统的状态,模式可以用连续时间离散状态的Markov过程来描述,在每一个模式中,状态可由一个随机微分方程表示。本文的主要内容包括如下几个方面:
1)针对含有Markov跳跃参数的线性不确定时滞系统研究了鲁棒保性能控制,鲁棒无源控制与鲁棒耗散控制问题。目标是设计控制器,使得对容许的不确定性,闭环系统是鲁棒稳定,并且满足所提的保性能指标,无源指标与耗散指标。基于Lyapunov稳定性理论给出了相应控制器的存在条件。进一步,将控制器的设计问题转化为LMI的求解问题。通过MATLAB中线性矩阵不等式工具箱可以很容易求得相应控制器的增益矩阵。
2)基于Lyapunov稳定性理论,将含有Markov跳跃参数的线性不确定时滞系统的鲁棒控制结果推广到含有Markov跳跃参数的中立型系统中。分别对鲁棒保性能控制,鲁棒无源控制与鲁棒耗散控制问题进行了研究。目标是设计控制器,使得闭环系统鲁棒稳定,并且分别满足所提的保性能指标,无源指标与耗散指标。通过对一组关联LMI的求解,获得了相应控制器的增益矩阵。
3)将含有Markov跳跃参数的线性不确定时滞系统的鲁棒控制结果推广到含有Markov跳跃参数的广义不确定时滞系统中。分别对鲁棒保性能控制,鲁棒H∞控制,鲁棒无源控制与鲁棒耗散控制问题进行了研究。目标是设计控制器,使得对容许的不确定性,闭环系统正则,无脉冲,且鲁棒稳定,并且分别满足
Because parameter varying is inevitable in practical systems, robust control for uncertain systems is not only significant for theory research but also valuable in practice. On the other hand, state estimation plays an important role in systems and control theory, signal processing and information fusion. Certainly, the most widely used estimation method is the well-known Kalman filtering. A common feature in the Kalman filtering is that an accurate model is available. In some applications, however, when the system is subject to parameter uncertainties, the accurate system model is difficult to be obtained. To overcome this difficulty, robust filtering approaches are proposed.
This dissertation mainly considers robust and filtering for time-delay systems with Markovian jumping parameters, neutral systems with Markovian jumping parameters and descriptor time-delay systems with Markovian jumping parameters based on Lyapunov stability theory. The proposed systems contain jumping parameters and uncertainties. The transition of jumping parameters in systems is governed by a finite-state Markov process. The class of systems is a hybrid class of systems with two components in the vector state. The first component refers to the mode and the second one to the state. The mode is described by a continuous Markov process with finite state space. The state in each mode is denoted by a stochastic differential equation. The main research results in this dissertation can be given as the following.
1) Robust guaranteed cost control, passive control, dissipative control for time-delay systems with Markovian jumping parameters are proposed. The objective is to design controllers such that for all uncertainties, the resulting closed system is robust stable and satisfies the proposed guaranteed cost, passive and dissipative performance, respectively. Based on Lyapunov stability theory, sufficient conditions on the existence of robust controllers are derived, respectively. Controllers are designed in terms of linear matrix inequalities. By using LMI toolbox in MATLAB, it is easily to obtain controllers gain matrices.
2) Based on Lyapunov stability theory, the results on robust control for time-delay systems with Markovian jumping parameters are extended to neutral
引文
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