System State Matrices Research Articles

Guaranteed Cost Finite-Time Control of Uncertain Coupled Neural Networks.

This article investigates a robust guaranteed cost finite-time control for coupled neural networks with parametric uncertainties. The parameter uncertainties are assumed to be time-varying norm bounded, which appears on the system state and input matrices. The robust guaranteed cost control laws presented in this article include both continuous feedback controllers and intermittent feedback controllers, which were rarely found in the literature. The proposed guaranteed cost finite-time control is designed in terms of a set of linear-matrix inequalities (LMIs) to steer the coupled neural networks to achieve finite-time synchronization with an upper bound of a guaranteed cost function. Furthermore, open-loop optimization problems are formulated to minimize the upper bound of the quadratic cost function and convergence time, it can obtain the optimal guaranteed cost periodically intermittent and continuous feedback control parameters. Finally, the proposed guaranteed cost periodically intermittent and continuous feedback control schemes are verified by simulations.

Subspace model identification under load disturbance with unknown transient and periodic dynamics

To overcome the influence from load disturbance with unknown transient and periodic dynamics, as often encountered when performing identification tests in engineering applications, a bias-eliminated subspace model identification method is proposed to realize consistent estimation, which can be used for both open- and closed-loop systems. By decomposing the output response into disturbed and undisturbed components, an oblique projection is subtly introduced to eliminate the disturbance and noise impact so as to obtain unbiased estimation on the deterministic system state matrices, while the disturbance response dynamics could be estimated. In particular, a specific algorithm based on minimizing the output prediction error is given to find out the disturbance period if exists, such that the disturbance effect can be eliminated by the above projection regardless of the disturbance waveform and magnitude. A shift-invariant approach is then given to retrieve the deterministic state matrices. Consistent estimation on the deterministic system matrices is analyzed with a proof. A benmark example from the literature and an industrial injection molding process are used to demonstrate the effectiveness and merit of the proposed method.

Time Integration-Based IGD Methods for Eigen-Analysis of Large Delayed Cyber-Physical Power System

Two spectral discretization methods based on linear multistep and implicit Runge-Kutta discretization of infinitesimal generator (IGD-LMS/IRK) are presented in this paper for eigen-analysis of large delayed cyber-physical power system (DCPPS) with large time delays. First, the whole delay interval is partitioned into several sub-intervals by time delays in the system. The piecewise partitioning allows the avoidance of interpolations in evaluating system states at the delay points. Second, two time integration methods, i.e., LMS and IRK, are utilized to discretize infinitesimal generator on each sub-interval, resulting in highly structured and sparse discretization matrices. Third, IGD-LMS/IRK are efficiently implemented to compute the system's electromechanical oscillation modes. The shift-invert preconditioning technique is used and the sparsity in augmented system state matrices is exploited to guarantee the efficiency and scalability of IGD-LMS/IRK in dealing with large DCPPS. Numerical results on the two-area four-machine test system and a real-life large transmission grid validate the improved efficiency and accuracy of the proposed methods in analyzing DCPPS with large time delays.

Eigen-Analysis of Large Delayed Cyber-Physical Power System by Time Integration-Based Solution Operator Discretization Methods

In this paper, solution operator discretization methods with linear multistep and implicit Runge–Kutta (SOD-LMS/IRK) are presented for efficient eigen-analysis of large delayed cyber-physical power system (DCPPS). First, the time integration-based discretization generates highly structured approximate matrices to the solution operator. Exploitation of the structure ensures low computational burden and high efficiency in solving the matrix-inversion-vector product involved in eigenvalue computation. Second, the implicitly restarted Arnoldi algorithm is employed to compute critical eigenvalue from the solution operator's discretized matrices. SOD-LMS/IRK are endowed with scalability in analyzing very large DCPPS by fully utilizing the inherent sparsity in the augmented system state matrices. The main contribution of the presented SOD-LMS/IRK is the improved efficiency and scalability of existing SOD-PS (pseudo-spectral collocation) and SOD-LMS/IRK. Numerical results on the 16-generator 68-bus test system, a 516-bus, and a 33028-bus real-life large transmission systems validate the effectiveness of the proposed SOD-LMS/IRK.

Online Analytical Characterization of Outliers in Synchrophasor Measurements: A Singular Value Perturbation Viewpoint

This paper presents a principal component (PC) analysis based method for online characterization of outliers in synchrophasor measurements. To that end, a linearized framework is established to analyze dynamical response from a system under nominal and off-nominal (e.g., faulted) conditions, which are contained in the same window of synchrophasor data. Inspired by the singular value perturbation theory, a bound on the change in the norm of the PC scores as a function of system state matrices is presented. It is shown that in the presence of bad data outliers these bounds for higher dimensional PC scores will be significantly larger compared to lower dimensions. The effect of the number of samples in the data window on the results of the analysis is established. Case studies on a simulated test system and on field data collected from a US utility are presented to support the analytical results. Finally, an online classifier for the characterization of outliers is developed to illustrate the usefulness of the proposed framework for machine learning based methods.

Implementation of extended Kalman filter-based simultaneous localization and mapping: a point feature approach

The implementation of extended Kalman filter-based simultaneous localization and mapping is challenging as the associated system state and covariance matrices along with the memory requirements become significantly large as the information space increases. Unique and consistent point features representing a segment of the map would be an optimal choice to control the size of covariance matrix and maximize the operating speed in a real-time scenario. A two-wheel differential drive mobile robot equipped with a Laser Range Finder with 0.02 m resolution was used for the implementation. Unique point features from the environment were extracted through an elegant line fitting algorithm, namely split only technique. Finally, the implementation showed remarkably good results with a success rate of 98% in feature identification and ±0.08 to ±0.11 m deviation in the generated map.

Iterative infinitesimal generator discretization-based method for eigen-analysis of large delayed cyber-physical power system

To efficiently analyze the stability of large delayed cyber-physical power systems (DCPPS) incorporating wide-area damping controllers, an iterative infinitesimal generator discretization-based method (IIGD) for computing critical eigenvalues of the system is presented. IIGD contains three core techniques to guarantee efficiency and scalability. First, the sparsity of the infinitesimal generator's discretized matrix, which possesses identical spectrum to DCPPS, is explored by reformulating its blocks into Kronecker products. Especially, the dominant block is factorized as sum of Kronecker products of constant Lagrange vectors and system state matrices, which lays the basis of further utilizing the sparsities in the augmented state matrices of DCPPS. Second, the shift-invert preconditioning technique is applied to transform the required eigenvalues into those dominated in moduli. Third, the inverse iteration of the discretized matrix involved in sparse eigenvalue computation is iteratively achieved by utilizing the induced dimension reduction method (IDR(s)). Subsequently, the discretized matrix–vector product embedded in the method is efficiently implemented by exploiting the unique property of Kronecker product and the inherent sparsities in augmented system state matrices. The correctness, accuracy, efficiency and scalability of IIGD are extensively studied and thoroughly validated on the two-area four-machine test system and a real-life large transmission grid.

Pulse compensation for PD-type iterative learning control against initial state shift

The rectangular pulse function is adopted to incorporate feed-forward compensation for various proportional-derivative-type iterative learning control updating laws applied to a class of linear time-invariant systems with initial state shift. The objective of pulse compensation is to suppress the tracking discrepancy incurred by initial state shift. By means of the generalised Young inequality of the convolution integral, the tracking performance of the pulse-based learning updating laws is analysed and the suppressive effect of the pulse compensation is evaluated by measuring the tracking error in the sense of Lebesgue-p norm. The derivation clarifies that the upper bound of the asymptotical tracking error can be improved by tuning the compensation gain properly though it is determined not only by the proportional and derivative learning gains but also by the system state, input and output matrices as well. Numerical simulations show that pulse compensation can effectively suppress the tracking error caused by initial state shift.

Almost Sure Stabilization of Uncertain Continuous-Time Markov Jump Linear Systems

This work deals with the robust almost sure (AS) stabilization problem for continuous-time Markov jump linear systems (MJLS). Norm-bounded uncertainties affecting the system state and input matrices are considered. A deterministically testable sufficient condition for robust AS stability is provided which relies on a bound on the 2-norm of the system transition matrix. Such a condition can be profitably employed also to design a robust feedback stabilization strategy. Such feedback design is based on a formulation of the sufficient condition for robust AS stability in terms of an equivalent LMI problem.

A High-Integrity Multivariable Robust Control With Application to a Process Control Rig

This brief presents a systematic approach for the design of a robust decoupling precompensator using an approximate right inverse (ARI) of a system, where the problem of finding an ARI is presented as an L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -gain minimization problem. Furthermore, new LMIs are presented to analyze worstcase L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -gain for an uncertain system. These LMIs use extra variables to eliminate product terms between system state matrices and the Lyapunov matrix. This elimination enables the use of a parameter dependent Lyapunov function in a systematic way. These LMIs are extended to synthesis both constant and dynamic precompensators as well. Using the synthesis and the analysis LMIs, a combined genetic-LMI-algorithm is also presented to find a suitable precompensator that achieves diagonal dominance for systems with input uncertainties. Some previously presented LMIs for pole clustering are also modified to make them compatible with newly presented LMIs. The proposed approach is applied to the design of a high integrity robust multiinput multioutput controller for a process control rig which consists of a temperature and a flow rate control loop. The system has an input uncertainty of about 20%. It is shown that the closed-loop system poses a high integrity while being robust with respect to input uncertainties. The controller is also applied to the real plant to verify that the proposed algorithm and the desired results are obtained.

Comparisons among robust stability criteria for linear systems with affine parameter uncertainties

This paper is concerned with the problem of comparisons among robust stability criteria for a class of uncertain linear systems, where the system state matrices considered are affinely dependent on the uncertain parameters. At first, a robust stability criterion for the class of systems to be affinely quadratically stable (AQS) is derived based on the vertex separator approach, where affine parameter-dependent Lyapunov functions are exploited to prove stability. Then comparison results between the robust stability criterion and the existing tests for AQS are given in terms of degree of conservatism. A numerical example is given to illustrate the results.

LMI Approach to Output Feedback Control for Linear Uncertain Systems with D-Stability Constraints

This paper deals with the problem of designing output feedback controllers for linear uncertain continuous-time and discrete-time systems with circular pole constraints. The uncertainty is assumed to be norm bounded and enters into both the system state and input matrices. We focus on the design of a dynamic output feedback controller that, for all admissible parameter uncertainties, assigns all the closed-loop poles inside a specified disk. It is shown that the problem addressed can be recast as a convex optimization problem characterized by linear matrix inequalities (LMI); therefore, an LMI approach is developed to derive the necessary and sufficient conditions for the existence of all desired dynamic output feedback controllers that achieve the specified circular pole constraints. An effective design procedure for the expected controllers is also presented. Finally, a numerical example is provided to show the usefulness and applicability of the present approach.

Controllability of inherently damped large flexible space structures

Graph theoretic techniques are used to study controllability of linear systems which could represent large flexible orbiting space systems with inherent damping. The controllability of the pair of matrices representing the system state and control influence matrices is assured when all states in the model are reachable in a digraph sense from at least one input and also when the term rank of a Boolean matrix whose non trivial components are based on the state and control influence matrices has a term rank of the order of the state vector. It is seen that the damping matrix does not influence the required number of actuators but gives flexibility to the possible locations of the actuators for which the system is controllable, and that the stiffness matrix term rank deficiency dictates the number as well as the location of the required actuators. Specific examples include a model of a shallow spherical orbiting shell where both orientation and shape control are required, and also a smaller dimensional numerical example (unrelated to the shell) which readily demonstrates the effect of damping.