时变系统遗忘因子最小二乘法的有界性收敛性

利用随机过程理论研究了遗忘因子最小二乘法（FFLS）的有界收敛性，给出了参数估计误差的上界，分析表明：i)对于时不变确定性系统；FFLS算法产生的参数估计以指数速度收敛于真参数；ii)对于时不变随机系统，FFLS算法给出界均方估计误差，iii)对于时变随机系统，FFLS算法可以跟踪时变参数，且跟踪误差有界。     

时变系统有限数据窗最小二乘辨识的有界收敛性

利用随机过程理论证明了有限数据窗最小二乘法的有界收敛性,给出了参数估计误差 上界的计算公式,阐述了获得最小均方参数估计误差上界时数据窗长度的选择方法.分析表明, 对于时不变随机系统,数据窗长度越大,均方参数估计误差上界越小;对于确定性时变系统,数 据窗长度越小,均方参数估计误差上界越小.因此,对于时变随机系统,一个折中方案是寻求一 个最佳数据窗长度,以使均方参数估计误差最小.该文的研究成果对于提高辨识算法的实际应 用效果有重要意义.     

时变系统最小均方算法的性能分析

在无过程数据平稳性假设和各态遍历等条件下,运用随机过程理论研究了最小方算法（LMS）的有界收敛性,给出了估计误差的上界,论述了LMS算法收敛因子或步长的选择方法,以使参数估计误差上界最小。这对于提高LMS算法的实际应用效果有着重要意义。LMS算法的收敛性分析表明：（1）对于确定性时不变系统,LMS算法是指数速度收敛的;（2）对于确定性时变系统,收敛因子等于1,LMS算法的参数估计误差上界最小;（3）对于时变或不变随机系统,LMS算法的参数估计误差一致有上界。     

时变参数遗忘梯度估计算法的收敛性

提出了时变随机系统的遗忘梯度辨识算法,并运用随机过程理论研究了算法的收敛性.分析表明,遗忘梯度算法的性能类似于遗忘因子最小二乘法,可以跟踪时变参数,但计算量要小得多,且数据的平稳性可以减小参数估计误差上界和提高辨识精度.阐述了最佳遗忘因子的选择方法,以获得最小参数估计上界.对于确定性时不变系统,遗忘梯度算法是指数速度收敛的;对于时变或时不变随机系统,遗忘梯度算法的参数估计误差一致有上界.     

一类线性时变系统组合自适应迭代学习辨识

针对一类在有限时间区间上可重复运行的既含时变参数又含时不变参数的高阶线性时变系统,提出了一种模型参考组合自适应迭代学习参数辨识算法.应用Lyapunov方法,给出了时不变参数的时域自适应学习律和时变参数的迭代域自适应学习律,分析了参数估计和模型状态跟踪误差的有界性与收敛性.该算法适于时变和时不变参数并存的线性系统的参数辨识,可加快参数估计的收敛速度.仿真例子验证了所提出的辨识算法的有效性.     

关于鞅超收敛定理与遗忘因子最小二乘算法的收敛性分析

鞅超收敛定理是研究随机时变系统辨识算法有界收敛性的一个有效数学工具,它是鞅收益是在随机时变系统中的推广。文「１」用它证明了遗忘因子最小二乘算法参数估计误差的有界收敛性,但是文「１」假设系统的理各态遍历的,且协方差阵是用它的数学期望代替的,所得到的结果是近似的。而本文精确地给出了协方差阵的上下界,改进了文「１」的结果。     

含有未知控制方向的非线性时滞系统学习控制

本文对于一类含有未知控制方向及时滞的非线性参数化系统,设计了自适应迭代学习控制算法.在设计控制算法过程中采用了参数分离技术和信号置换思想来处理系统中出现的时滞项,Nussbaum增益技术解决未知控制方向等问题.为了对系统中出现的未知时变参数和时不变参数进行估计,分别设计了差分及微分参数学习律.然后通过构造的Lyapunov-Krasovskii复合能量函数给出了系统跟踪误差渐近收敛及闭环系统中所有信号有界的条件.最后通过一个仿真例子说明了控制器设计的有效性.     

多丢包不确定离散系统的鲁棒Kalman滤波

研究了同时具有不确定性和多丢包情况下的离散时变系统的鲁棒滤波问题, 其中的不确定性是时变的、范数有界的, 且存在于系统的状态矩阵和输出矩阵中. 通过把多丢包问题建模成系统模型中的随机参数, 在允许的不确定性情况下, 给出了估计误差方差的上界, 并进一步基于矩阵范数的意义最小化该上界. 结果表明, 通过求解两个Riccati差分方程, 可以设计鲁棒滤波器. 最后, 提出适合在线计算的鲁棒滤波算法, 并通过仿真实例表明所提算法的有效性和实用性.     

带有干扰的时变系统的变结构鲁棒控制

对含有未知时变参数和外界干扰的单输入单输出线性时变系统,给出了一种变结构鲁棒输出跟踪控制器.系统参数不限定为慢时变或者结构已知的,只要求光滑有界且所需高阶导数有界.通过引入辅助信号和带有记忆功能的正规化信号,以及适当选择控制器参数,该变结构控制器能保证闭环系统所有信号的有界性,跟踪误差能被调整到任意小的范围内.     

高阶参数优化迭代学习控制算法

针对线性时不变离散系统的跟踪问题提出一种高阶参数优化迭代学习控制算法.该算法通过建立考虑了多次迭代误差影响的参数优化目标函数,求解得出优化后的时变学习增益参数.从理论上证明了:对于线性离散时不变系统,该算法在被控对象不满足正定性的松弛条件下仍可保证跟踪误差单调收敛于零.同时,采用之前多次迭代信息的高阶算法具有更好的收敛性和鲁棒性.最后利用一个仿真实例验证了算法的有效性.     

鞅超收敛定理与遗忘因子最小二乘算法的收敛法分析

本文扩展了用于分析时不变系统辨识算法收敛性的鞅收敛定理，建立了鞅超收敛定理。它可以作为工具来分析时变系统的各种辨识算法的收敛性，为地变系统收敛性和稳定性分析这一困难课题提供了新方法，开辟了新路。     

Adaptive control of linear time-varying plants: a new modelreference controller structure

The problem of developing a control law which can force the output of a linear time-varying plant to track the output of a stable linear time-invariant reference model is discussed. It is shown that the standard model reference controller, used for linear time-invariant plants, cannot guarantee zero tracking error in general when the plant is time-varying. A new model reference controller is proposed which guarantees stability and zero tracking error for a general class of linear time-varying plants with known parameters. When the time-varying plant parameters are unknown but vary slowly with time, it is shown that the new controller can be combined with a suitable adaptive law so that all the signals in the closed loop remain bounded for any bounded initial conditions and the tracking error is small in the mean. The assumption of slow parameter variations in the adaptive case can be relaxed if some information about the frequency or the form of the fast varying parameters is available a priori. Such information can be incorporated in an appropriately designed adaptive law so that stability and improved tracking performance is guaranteed for a class of plants with fast varying parameters     

Adaptive tracking control for stochastic uncertain non-linear systems satisfying short- and long-term cost criteria

The tracking control problem for a class of stochastic and uncertain non-linear systems is addressed. The proposed controller uses suitable radial basis function neural network designs for the approximation of the unknown non-linearities while it is arbitrarily regulated in order to effectively penalize the tracking error. This regulation is implemented through a risk-sensitivity parameter. A stability analysis based on Lyapunov functions obtained by the backstepping technique, proves that all the error variables are bounded in probability; simultaneously, for any given risk-sensitivity parameter the system performance is regulated with respect to both a desired small average tracking error and low long-term average cost in accordance to a risk-sensitive cost criterion. Moreover, the larger this parameter is, the mean square tracking error becomes semiglobally uniformly ultimately bounded in a smaller area while a lower level of a long-term average cost is achieved. The effectiveness of the design approach is illustrated by simulation results wherein it becomes clear how one can achieve a tradeoff between good response and control effort.     

随机多智能体系统一致性增益的设计与分析

在固定和切换拓扑中通信网络含有加性随机噪声的情况下,针对随机多智能体系统一致性跟踪控制问题,本文采用自适应控制方法给出了一种新的一致性增益设计方法.在基于邻居智能体状态设计的分布式自适应控制协议中,每个跟随者的一致性增益自适应律仅仅依赖于跟踪误差,并且与通信网络全局信息无关.结合代数图论,随机理论工具和自适应控制得到两个结论:1)每个跟随者以均方意义下跟踪上领导者; 2)每个跟随者的一致性增益趋于一个理想估计值.通过两个仿真实例验证算法的有效性.     

辨识时变系统遗忘因子算法的收敛性分析

著名的递推遗忘因子算法（ＲＦＦＡ）可以用辨识时变系统参数，具有良好的跟踪性能，本文借助于随机过程理论分析了ＲＦＦＡ的收敛性和稳定性，给出了参数跟踪误差的上下界。     

Performance analysis of multi-innovation stochastic Newton recursive algorithms

The stochastic Newton recursive algorithm is studied for system identification. The main advantage of this algorithm is that it has extensive form and may embrace more performance with flexible parameters. The primary problem is that the sample covariance matrix may be singular with numbers of model parameters and (or) no general input signal; such a situation hinders the identification process. Thus, the main contribution is adopting multi-innovation to correct the parameter estimation. This simple approach has been proven to solve the problem effectively and improve the identification accuracy. Combined with multi-innovation theory, two improved stochastic Newton recursive algorithms are then proposed for time-invariant and time-varying systems. The expressions of the parameter estimation error bounds have been derived via convergence analysis. The consistence and bounded convergence conclusions of the corresponding algorithms are drawn in detail, and the effect from innovation length and forgetting factor on the convergence property has been explained. The final illustrative examples demonstrate the effectiveness and the convergence properties of the recursive algorithms.     

Adaptive control of linear time-varying systems

Single-input single-output uncertain linear time-varying systems are considered, which are affected by unknown bounded additive disturbances; the uncertain time-varying parameters are required to be smooth and bounded but are neither required to be sufficiently slow nor to have known bounds. The output, which is the only measured variable, is required to track a given smooth bounded reference trajectory. The undisturbed system is assumed to be minimum-phase and to have known and constant relative degree, known sign of the ‘high frequency gain’, known upper bound on the system order. An adaptive output feedback control algorithm is designed which assures: (i) boundedness of all closed-loop signals; (ii) arbitrarily improved transient performance of the tracking error; (iii) asymptotically vanishing tracking error when parameter time derivatives are L₁ signals and disturbances are L₂ signals.     

On the adaptive control of a class of systems with random parameters and disturbances

The adaptive control of discrete time parameter linear stochastic systems with random parameters is investigated. It is shown that systems whose (unknown) autoregressive parameters undergo bounded martingale difference disturbances may be stabilized by the application of the so-called Modified Least Squares adaptive control algorithm. Asymptotically, the sample mean square performance criterion is equal to the one step ahead minimum variance control loss (which equals the prediction error variance when the system parameters are known) plus a term which is bounded by a quantity proportional to the square of the bound on the parameter disturbance. This latter term may be interpreted as the increase in the prediction error variance due to the random parameter variation.