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.     

反馈非线性系统随机梯度辨识算法及其收敛性

反馈非线性受控自回归系统是由前向通道的受控自回归模型和反馈通道的静态非线性构成, 这类系统经过参数化后得到双线性参数辨识模型. 本文通过对辨识模型中双线性参数乘积项进行分解, 基于梯度搜索原理, 提 出了反馈非线性系统的随机梯度辨识算法. 为了改善随机梯度算法的收敛速度, 引入遗忘因子, 文章给出了遗忘因子随机梯度算法, 利用随机过程理论, 建立了随机梯度算法的参数估计收敛定理, 证明了算法的收敛性. 最后, 通过数值仿真验证了算法的有效性.     

Identification of time‐varying OE models in presence of non‐Gaussian noise: Application to pneumatic servo drives

Intensive research in the field of mathematical modeling of pneumatic servo drives has shown that their mathematical models are nonlinear in which many important details cannot be included in the model. Owing the influence of the combination of heat coefficient, unknown discharge coefficient, and change of temperature, it was supposed that parameters of the pneumatic cylinder are random (stochastic parameters). On the other side, it has been well known that the nonlinear model can be approximated by a linear model with time‐varying parameters. Due to the aforementioned reasons, it can be assumed that the pneumatic cylinder model is a linear stochastic model with variable parameters. In practical conditions, in measurements, there are rare, inconsistent observations with the largest part of population of observations (outliers). Therefore, synthesis of robust algorithms is of primary interest. In this paper, the robust recursive algorithm for output error models with time‐varying parameters is proposed. The convergence property of the proposed robust algorithm is analyzed using the methodology of an associated ordinary differential equation system. Because ad hoc selection of model orders leads to overparameterization or parsimony problem, the robust Akaike's criterion is proposed to overcome these problems. By determining the least favorable probability density for a given class of probability distribution represents a base for design of the robust version of Akaike's criterion. The behavior of the proposed robust identification algorithm is considered through intensive simulations that demonstrate the superiority of the robust algorithm in relation to the linear algorithms (derived under an assumption that the stochastic disturbance has a Gaussian distribution). The good practical values of the proposed robust algorithm to identification of the pneumatic cylinder are illustrated by experimental results. Copyright © 2016 John Wiley & Sons, Ltd.     

Adaptive control of a simple time-varying system

Adaptive control of a first-order randomly varying stochastic process is considered. Several authors have treated this problem using either ergodic theory for Markov processes or martingale limit theorems. In both cases some initial variance calculations and bounds evaluations must be performed in order to apply these techniques and establish the sample path results generally considered in adaptive control. These prior calculations are performed in the more general case where the single parameter follows a random walk and for an identification algorithm requiring no a priori knowledge of noise characteristics     

Optimal Deterministic and Stochastic Macroeconomic Policies for Slovenia: An Application of the OPTCON Algorithm

This paper reports about applications of optimal control theory to the analysis of macroeconomic policies for Slovenia during its way into the Euro Area. For this purpose, the model SLOPOL4, a macroeconometric model for Slovenia, is used. Optimal policies are calculated using the OPTCON algorithm, an algorithm for determining (approximately) optimal solutions to deterministic and stochastic control problems. We determine optimal exchange rate and fiscal policies for Slovenia as solutions to optimum control problems with a quadratic objective function and the model SLOPOL4 as constraint. Several optimization experiments under different assumptions about the exchange rate regime are carried out. The sensitivity of the results with respect to several assumptions is investigated; in particular, the reaction of the optimal paths on varying the stochastic character of the model parameters is examined. If the stochastic nature of more parameters is taken into consideration, the resulting policies are closer to the deterministic solution than with only a few stochastic parameters.     

Mean-square-deviation analysis of probabilistic LMS algorithm

A stochastic analysis of the probabilistic least-mean-square (Prob-LMS) algorithm would be a useful guideline for designing the adaptive filter. However, no analytical expressions for the stochastic analysis of the Prob-LMS algorithm have been reported in the literature. Hence, this paper analyzes the mean-deviation and mean-square-deviation (MSD) behavior of the Prob-LMS algorithm for the general case of an unknown Gauss-Markov channel. Analytical expressions are derived for the transient and steady-state MSD of the Prob-LMS algorithm. Monte Carlo simulations for fixed and time varying channels show excellent agreement between the simulated and theoretical MSD for a wide range of parameters such as SNR, filter length and input signal statistics. Monte Carlo MSD simulation results are presented for the Prob-LMS algorithm which compare favorably to several well-known VSS algorithms.     

A new form of the extended Kalman filter for parameter estimation in linear systems with correlated noise

A well-known method for estimation of parameters in linear systems with correlated noise is the extended Kalman filter where the unknown parameters are estimated as a part of an enlarged state vector. To avoid the computational burden in determining the state estimates when only the parameter estimates are required, a new simple form of the extended Kalman filter, where the state consists only of the parameters to be estimated, is proposed. The algorithm is based on the inclusion of the computed residuals in the observation matrix of a state representation of the system, an idea first introduced in the so-called extended least-squares or Panuska's method. Convergence properties of the proposed algorithm are studied, and the algorithm is shown to perform a gradient-based minimization of the maximum likelihood loss function. Some special cases of the algorithm are also discussed, and an extension to an estimator for randomly varying parameters is outlined.     

Modified stochastic gradient parameter estimation algorithms for a nonlinear two-variable difference system

This paper proposes a stochastic gradient algorithm and two modified stochastic gradient algorithms for a nonlinear two-variable difference system. The output and the input of a two-variable parameter system depend on time and on spatial coordinates. A stochastic gradient algorithm is introduced to estimate the unknown parameters. In order to increase the convergence rate but not to increase the computational effort, two modified stochastic gradient algorithms are also proposed. The simulation results indicate that the proposed methods are effective.     

Global output feedback regulation of nonlinear time delay systems subject to sensor measurement faults

This article studied the global output feedback regulation problem for a class of uncertain nonlinear time delay systems subject to unknown measurement faults on sensors. Different from the existing works, we consider the unknown time‐varying delays on the system states and relax their conservative condition on nonlinear functions. By introducing two novel time‐varying gains, a new global output feedback regulation algorithm is proposed, which ensures control parameters can be chosen flexibly. The proposed linear‐like controller is independent of the unknown time‐varying delays. Moreover, it has a simple structure, which is convenient for the implementation in practice. Based on the Lyapunov stability theory, it is strictly proved that all signals of the resulting closed‐loop system are globally bounded with the designed controller. Finally, a simulation example is presented to illustrate the effectiveness of the proposed output feedback regulation algorithm.     

Further criterion for stochastic stability analysis of semi‐Markovian jump linear systems

This article is devoted to provide further criterion for stochastic stability analysis of semi‐Markovian jump linear systems (S‐MJLSs), in which more generic transition rates (TRs) will be studied. As is known, the time‐varying TR is one of the key issues to be considered in the analysis of S‐MJLS. Therefore, this article is to investigate general cases for the TRs that covered almost all types, especially for the type that the jumping information from one mode to another is fully unknown, which is merely investigated before. By virtue of stochastic functional theory, sufficient conditions are developed to check stochastic stability of the underlying systems via linear matrix inequalities formulation combined with a maximum optimization algorithm. Finally, a numerical example is given to verify the validity and effectiveness of the obtained results.     

具有学习特点的控制器设计算法

对于普遍存在的具有未知参数的随机最优控制问题,本文提出了一种具有学习特点的控制器设计算法.该算法用Kalman滤波估计系统的未知参数,在滚动优化机制下用动态规划获取控制增益,为了赋予控制器的学习特点,在LQG控制律中附加使下一时刻估计方差最小的学习控制分量.仿真结果表明了算法的有效性.     

Optimal filtering in stochastic discrete-time systems with unknowninputs

In this note we derive a recursive filtering algorithm for the linear discrete-time dynamic system with indeterminate-stochastic inputs. The algorithm is based on the minimax-optimal method of parameter estimation in the linear regression model with parameters of two different types: unknown and stochastic with partially known characteristics     

A GRADIENT BASED ADAPTIVE CONTROL ALGORITHM FOR DUAL‐RATE SYSTEMS

In this paper, using a polynomial transformation technique, we derive a mathematical model for dual‐rate systems. Based on this model, we use a stochastic gradient algorithm to estimate unknown parameters directly from the dual‐rate input‐output data, and then establish an adaptive control algorithm for dual‐rate systems. We prove that the parameter estimation error converges to zero under persistent excitation, and the parameter estimation based control algorithm can achieve virtually asymptotically optimal control and ensure the closed‐loop systems to be stable and globally convergent. The simulation results are included.     

Synchronization of unknown chaotic neural networks with stochastic perturbation and time delay in the leakage term based on adaptive control and parameter identification

In this paper, we investigate the synchronization problem of chaotic neural networks with unknown parameters, stochastic perturbation and time delay in the leakage term. A simple and robust adaptive controller is designed such that the response system can be synchronized with a drive system with unknown parameters by utilizing Lyapunov stability theory and parameter identification. Our synchronization criteria are easily verified and do not need to solve any linear matrix inequality. This research also demonstrates the effectiveness of application in secure communication. Numerical simulations are carried out to illustrate the main results.     

多自由度遥操作机器人可靠性控制研究

本文针对多自由度遥操作机器人的可靠性控制问题进行了研究,采用时延估计在线获得机器人系统的未知动力学和外界干扰,并在控制过程中加以补偿.这里,我们利用一些满足一定概率分布的不相关的随机变量来表示遥操作机器人的概率性执行器故障.通过考虑遥操作机器人的概率性执行器故障和控制时变时延,我们建立了新的遥操作机器人模型.在此基础上,研究了遥操作机器人的可靠性控制.通过使用Lyapunov稳定性方法和随机系统理论,得到了遥操作机器人的执行器概率分布依赖的渐近均方稳定的充分性条件,其中该条件是以线性矩阵不等式的形式给出,从而非常便于计算机转化为凸优化问题进行求解.最后用一个仿真算例来验证本文给出方法具有以下作用:首先,在考虑遥操作机器人的概率性执行器的故障的情况下,本文提出方法可以很容易地得到控制输入时延的上界;其次,在不考虑遥操作机器人执行器故障时,本文提出方法依然可以使用;最后,在考虑遥操作机器人的概率性执行器故障时,本文提出的方法都可以为其设计理想的控制器.     

The extended minimal controller synthesis algorithm

In a previous paper (Benchoubane and Stoten 1992) we noted that the minimal control synthesis (MCS) algorithm, when applied to the control of plant with rapidly varying disturbances, could lead to stable, but only bounded, error dynamics. The purpose of this paper is to show that, with some modification, MCS can elicit global asymptotically stable error dynamics, even in the presence of rapidly varying disturbances. We label the modified algorithm as the extended minimal control synthesis (EMCS) algorithm. Disturbances include plant parameter variations, external inputs and plant nonlinearities. In common with the general philosophy behind MCS, we assume that all nominal plant parameters and disturbance parameters are unknown. Two examples of EMCS implementations—one for a SISO plant and the other for a MIMO plant —are included in the paper to demonstrate the effectiveness, and practical aspects, of this new algorithm.     

An image encryption algorithm based on Baker map with varying parameter

Because of the excellent properties, such as unpredictability, randomness, aperiodicity, sensitive dependence on initial conditions and parameters, chaotic systems become popular in security applications. However, for a fixed chaotic system, with the development of chaos theory, the chaotic orbits may be estimated and their parameters or initial values may be predicted. In this paper, we introduce a parameter-varying Baker map (PVBM), whose output signal is non-stationary. The varying parameters disrupt the phase space of the system, which can resist the phase space reconstruction attacks and chaotic signal estimation technologies effectively. To investigate its applications, we propose a new image encryption algorithm, which is combined with chaotic shuffling and chaotic substitution. Simulation results demonstrate the proposed algorithm have high security as well as to resist various attacks.     

Automatic modeling algorithm of stochastic error for inertial sensors

This paper proposes an automatic algorithm to determine the properties of stochastic processes and their parameters for inertial error. The proposed approach is based on a recently developed method called the generalized method of wavelet moments (GMWM), whose estimator was proven to be consistent and asymptotically normally distributed. This algorithm is suitable mainly (but not only) for the combination of several stochastic processes, where the model identification and parameter estimation are quite difficult for the traditional methods, such as the Allan variance and the power spectral density analysis. This algorithm further explores the complete stochastic error models and the candidate model ranking criterion to realize automatic model identification and determination. The best model is selected by making the trade-off between the model accuracy and the model complexity. The validation of this approach is verified by practical examples of model selection for MEMS-IMUs (micro-electro-mechanical system inertial measurement units) in varying dynamic conditions.     

Decision theoretic approach to real-time robust identification

A decision-theoretic approach to the estimation of unknown parameters from a linear discrete-time dynamic measurement model in the presence of disturbance uncertainty is considered. The unknown disturbance statistics are characterized by a certain class of distributions to which the real disturbance distribution is confined. Using game theory and the asymptotic estimation error covariance matrix as the criteria of how good an estimator is, the stochastic gradient-type algorithm is shown to be optimal in the min-max sense. Since the optimal solution is not tractable in practice, several suboptimal procedures are derived on the basis of suitable approximations. The convergence of the derived algorithms is established theoretically using the ordinary differential equation approach. Monte Carlo simulation results are presented for the quantitative performance evaluation of the algorithms.     

Identification of Systems With Regime Switching and Unmodeled Dynamics

This paper is concerned with persistent identification of systems that involve deterministic unmodeled dynamics and stochastic observation disturbances, and whose unknown parameters switch values (possibly large jumps) that can be represented by a Markov chain. Two classes of problems are considered. In the first class, the switching parameters are stochastic processes modeled by irreducible and aperiodic Markov chains with transition rates sufficiently faster than adaptation rates of the identification algorithms. In this case, tracking real-time parameters by output observations becomes impossible and we show that an averaged behavior of the parameter process can be derived from the stationary measure of the Markov chain and can be estimated with periodic inputs and least-squares type algorithms. Upper and lower error bounds are established that explicitly show impact of unmodeled dynamics. In contrast, the second class of problems represents systems whose state transitions occur infrequently. An adaptive algorithm with variable step sizes is introduced for tracking the time-varying parameters. Convergence and error bounds are derived. Numerical results are presented to illustrate the performance of the algorithm.