Minimal order observers for estimating linear functions of a state vector

This paper studies the necessary and sufficient conditions for a pth-order observer to observe linear functions of the states of a linear dynamical system. The conditions are a set of multivariable polynomial equations which must be satisfied for some variable set in order for a pth-ncder observer to exist. It is possible to test for the existence of such a variable set in a finite number of steps via decision methods and thereby to construct an observer with the aid of polynomial factorization. To minimize the computational effort, the necessary and sufficient conditions are expressed in terms of the minimum number of variables.     

An algorithm for estimating a portion of the state vector

An algorithm is developed for estimating a portion of the state of a linear dynamical system. The dimension of the filter used in the estimation procedure may be considerably smaller than the dimension of a Kalman filter used to estimate the entire state vector. Thus, an on line computational advantage is achieved. The savings may be significant if the dimension of the segment of the state vector which is of interest is much smaller than the dimension of the entire state vector.     

基于状态观测器的线性不确定时滞系统的保代价控制

研究一类线性不确定时滞系统，基于状态观测器给出了系统保代价控制的无记忆状态反馈控制器，并给出了保代价控制器存在的充分条件，在某些条件满足的条件下，基于LMI给出了系统保代价控制器。     

On terminal optimal linear filtering of a convolution of the state vector of an information process

An approach to forming an algorithmic technique of terminal optimal linear filtering of characteristics of the state vector of reduced dimension based on the use of the properties of the projection of the Hamiltonian system following the Riccati equation is addressed. An estimate of the computational efficiency is given. The process of finding terminal estimates is illustrated.     

线性分式不确定系统保成本控制及其鲁棒界

研究线性分式不确定系统的动态输出反馈保成本控制.采用线性矩阵不等式(LMI)方法证明了保成本控制器存在的充分必要条件等价于一个LMI可解性问题,通过该条件将求解闭环系统的成本函数上界的最小值问题转化为一个凸优化问题,利用该凸优化问题的解,得到动态输出反馈控制器的增益矩阵,并且给出了摄动参数允许最大摄动界的一种算法.     

A technique for estimating the state of a nonlinear system

A technique for the estimation of the state of a general class of nonlinear systems is discussed. The technique involves linear optimal estimation of the state of a linear approximation to the nonlinear system. The linear approximation to the nonlinear system is derived solely from the nonlinear differential equations and the noise-corrupted observations of some of the components of the state vector of the nonlinear system. An example of optimal estimation of the current position and velocity of a low earth-orbit satellite, using range, elevation and azimuth observations from a ground tracking station, is discussed. Numerical results from a digital simulation of the example are presented.     

Successive identification of the random-parameter linear dynamic system

For the case of unknown parameters that are subject to noise, a successive algorithm for identification of the discrete-time linear stochastic system was proposed. Special selection of a random instant of observation abortion in the least-squares method enabled determination of the theoretical boundary of the root-mean-square precision of the vector estimator which is inversely proportional to the procedure parameter defining its duration. The results of numerical modeling were presented.     

The state vector reconstruction for linear systems with unknown inputs

Necessary and sufficient conditions for the existence of an observer for linear multivariable systems with unknown inputs are presented in Theorem 1. Proof of the theorem gives an algorithm of full order observer matrices calculation.     

Neural network-based discrete-time Z-type model of high accuracy in noisy environments for solving dynamic system of linear equations

To solve dynamic system of linear equations with square or rectangular system matrices in real time, a discrete-time Z-type model based on neural network is proposed and investigated. It is developed from and studied with the aid of a unified continuous-time Z-type model. Note that the framework of such a unified continuous-time Z-type model is generic and has a wide range of applications, such as robotic redundancy resolution with quadratic programming formulations. To do so, a one-step-ahead numerical differentiation formula and its optimal sampling-gap rule in noisy environments are presented. We compare the Z-type model extensively with E-type and N-type models. Theoretical results on stability and convergence are provided which show that the maximal steady-state residual errors of the Z-type, E-type and N-type models have orders \(O(\tau ^3)\), \(O(\tau ^2)\) and \(O(\tau )\), respectively, where \(\tau \) is the sampling gap. We also prove that the residual error of any static method that does not exploit the time-derivative information of a time-dependent system of linear equations has order \(O(\tau )\) when applied to solve discrete real-time dynamic system of linear equations. Finally, several illustrative numerical experiments in noisy environments as well as two application examples to the inverse-kinematics control of redundant manipulators are provided and illustrated. Our analysis substantiates the efficacy of the Z-type model for solving the dynamic system of linear equations in real time.

     

Bayesian robust linear dynamic system approach for dynamic process monitoring

In this paper, a Bayesian robust linear dynamic system approach is proposed for process modeling. Traditional linear dynamic system (LDS) constructed with Kalman filter is designed by Gaussian assumption which can be easily violated in non-Gaussian modeling situations, especially those with outliers. To deal with this issue, the conventional Gaussian-based Kalman filter is modified with heavy tailed Student's t-distribution so as to deal with the non-Gaussian noise and modeling outliers. Then, a variational Bayesian expectation maximization (VBEM) algorithm is developed for learning parameters of the robust linear dynamic system. For process monitoring, traditional monitoring scheme are discussed and the residual space monitoring mechanism has been improved. To explore the feasibility and effectiveness, the proposed method is applied for fault detection, with detailed comparative studies with several other methods through the Tennessee Eastman benchmark.     

Optimal technique for estimating the reachable set of a controlled n-dimensional linear system

The reachable set from a given point of a controlled dynamical system is the set of all states to which the system can be driven from that point in a finite time by the allowed controls. A technique is presented Tor estimating the reachable set from the asymptotically-stable origin of a class of n-dimensional linear systems under bounded control. The technique is an optimal version of a Lyapunov method, and provides an (over-)estimate of the full reachable set; it involves the minimization of a quadratic constraint, followed by the maximization of a quadratic form subject to this constraint. The non-linear optimization problems can be routinely solved by means of computer algebra and commonly available computer software. In general, the technique produces a much-improved estimate of the reachable set compared to that given by the standard Lyapunov method. Another advantage of the technique is that it is truly applicable to higher-dimensional systems (n ≥ 3). Since the estimate produced is in the convenient form of an n-dimensional ellipsoid, projections of the estimate onto any space of dimension ≤ n — 1 can be readily found. Problems of two, three, and four dimensions are solved to illustrate the technique.     

Brain activity detection by estimating the signal-to-noise ratio of fMRI time series using dynamic linear models

This work shows an example of the application of Bayesian dynamic linear models in fMRI analysis. Estimating the error variances of such a model, we are able to obtain samples from the posterior distribution of the signal-to-noise ratio for each voxel, which is used as a criterion for the detection of brain activity. The benefits of this approach are: (i) the reduced number of parameters, (ii) the model makes no assumptions about the stimulation paradigm, (iii) an interpretable model based approach, and (iv) flexibility. The performance of the proposed method is shown by simulations and further results are presented on the application of the model for the analysis of a real fMRI data set, in order to illustrate some practical issues and to compare with previously proposed techniques. The results obtained demonstrate the ability of the model to detect brain activity, even when the stimulus paradigm is unknown, constituting an alternative to data driven approaches when dealing with resting-state fMRI.     

A dynamic state estimator for power system dynamic security assessment

A global modularized dynamic state estimator is formulated to provide the data which will be required for future dynamic security assessment and dynamic security enhancement applications. The dynamic state estimator is global because it is capable of estimating small and large dynamic fluctuations in voltage angle and frequency for an entire area. The dynamic state estimator is composed of the sum of the static state estimate, obtained by using present hardware and algorithms and a modularized dynamic state estimate based on a linearized classical transient stability model with a stochastic load model. This dynamic state estimate component is modularized to (1) eliminate the need to measure or model external system generation and (2) to permit a reduction in computation requirements for (a) updating the linearized power system dynamic model and (b) for computing the state estimate. The modularization, which is accomplished by decoupling the linearized dynamic model for each subregion by measuring the power injections on lines connecting the subregion to the rest of the power system, causes the dynamic state estimate to be locally referenced. A global referencing procedure is proposed and discussed. A linearized stochastic model for the Michigan Electric Coordinated System is developed to illustrate the procedures proposed for developing the stochastic load model and determining the constant gain approximation for the governor turbine energy system dynamics. A summary of results on the performance of the Kalman state estimator is presented.     

永磁直线同步电机矢量控制模型的 优化与准确性分析

基于永磁直线同步电机数学模型,构建具有三闭环控制结构的永磁直线同步电机伺服控制系统,并采用电压空间矢量控制策略,在MatLab/Simulink环境下搭建永磁直线同步电机伺服控制系统整体仿真模型,通过对仿真实验结果的分析,表明了该模型的正确性,为后续高精度永磁直线同步电机控制方法的研究提供了基础模型.     

Constructing an analogue of the Kalman filter for a guaranteed state estimation of a dynamic system

A filter similar to the known Kalman filter is constructed to obtain the external guaranteed ellipsoidal estimate of the state of a dynamic system using measurements. Information on uncertain factors acting upon the system and observation errors is supposed to be restricted to knowing the boundaries of possible values of these variables. A numeric example of how the obtained relations can be used is given.     

Recursive transformation matrices for linear dynamic system models

In time series analyses and forecasting, dynamic linear models of canonical form are quite often used, specially in Generalised Exponentially Weighted Regression (GEWR) type models, introduced by Harrison and Akram (1982) and Akram (1984). This form is convenient, but usually not attractive for operation since the meaning of the parameters is not clear. To overcome this problem one needs a system of dynamic linear models in diagonal or any other meaningful form similar to canonical form. This is obtained by reparameterisation of a model to a desired form by similarity transformation of one system to another system through a transformation matrix. A general analytical expression for the elements of this matrix and its inverse, specially in case of canonical to diagonal transformation, is not known. One needs to compute these elements each time a transformation is sought. To ease this cumbersome problem a general recursive form of transformation matrix along with its inverse is presented for canonical to diagonal transformation. This general result apart from simplifying the process of transformation of linear dynamic systems helps us to reparameterise the models to a desired form.     

Stabilizing a linear system with quantized state feedback

The problem of stabilizing an unstable, time-invariant, discrete-time, linear system by means of state feedback when the measurements of the state are quantized is addressed. It is found that there is no control strategy that stabilizes the system in the traditional sense of making all closed-loop trajectories asymptotic to zero. If the system is not excessively unstable, feedback strategies that bring closed-loop trajectories arbitrarily close to zero for a long time can be implemented. It is also found that when the ordinary linear feedback of quantized state measurements is applied, the resulting closed-loop system behaves chaotically. The asymptotic pseudorandom closed-loop system dynamics differ substantially from what would be predicted by a conventional signal-with-noise analysis of the quantization's effects. Probabilistic reformulations of the stability problem in terms of the invariant measure are considered     

Software testing processes as a linear dynamic system

Software testing is essential for software reliability improvement and assurance, and the processes of software testing are intrinsically dynamic. However they are seldom investigated in a mathematically rigorous manner. In this paper a theoretical study is presented to examine the dynamic behavior of software testing. More specifically, a set of simplifying assumptions is adopted to formulate and quantify the software testing processes. The mathematical formulae for the expected number of observed software failures are rigorously derived, the bounds and trends of the expected number of observed software failures are analyzed, and the variance of the number of observed software failures is examined. On the other hand, it is demonstrated that under the simplifying assumptions, the software testing processes can be treated as a linear dynamic system. This suggests that the software testing processes could be classified as linear or non-linear, and there be intrinsic link between software testing and system dynamics.     

A framework for simulating and estimating the state and functional topology of complex dynamic geometric networks

We introduce a framework for simulating signal propagation in geometric networks (networks that can be mapped to geometric graphs in some space) and developing algorithms that estimate (i.e., map) the state and functional topology of complex dynamic geometric networks. Within the framework, we define the key features typically present in such networks and of particular relevance to biological cellular neural networks: dynamics, signaling, observation, and control. The framework is particularly well suited for estimating functional connectivity in cellular neural networks from experimentally observable data and has been implemented using graphics processing unit high-performance computing. Computationally, the framework can simulate cellular network signaling close to or faster than real time. We further propose a standard test set of networks to measure performance and compare different mapping algorithms.