On the aggregation of linear discrete-time invariant stochastic systems

For the multisensor linear discrete time‐invariant stochastic systems with unknown noise variances, using the correlation method, the information fusion noise variance estimators with consistency are given by taking the average of the local noise variance estimators. Substituting them into two optimal weighted measurement fusion steady‐state Kalman filters, two new self‐tuning weighted measurement fusion Kalman filters with a self‐tuning Riccati equation are presented. By the dynamic variance error system analysis (DVESA) method, it is rigorously proved that the self‐tuning Riccati equation converges to the steady‐state optimal Riccati equation. Further, by the dynamic error system analysis (DESA) method, it is proved that the steady‐state optimal and self‐tuning Kalman fusers converge to the global optimal centralized Kalman fuser, so that they have the asymptotic global optimality. Compared with the centralized Kalman fuser, they can significantly reduce the computational burden. A simulation example for the target tracking systems shows their effectiveness. Copyright © 2010 John Wiley & Sons, Ltd.

The problem of intermittent fault (IF) detection is studied for a class of linear discrete-time stochastic systems with unknown disturbance under the influence of a class of networked phenomena by using the moving horizon estimation (MHE). Aiming to normalise the transmission of data in network systems, the Round-Robin (RR) protocol is introduced for linear discrete-time stochastic systems, so the system is converted to a linear periodic system. By using the lifting technique and superposition principle, the linear periodic discrete-time system is transformed into a linear discrete time-invariant system. An MHE strategy is developed to cope with unknown disturbance by introducing provisional estimates of external unknown disturbances. By utilizing the moving horizon estimator, a scalar residual decoupled from the unknown disturbance is designed. Finally, the effectiveness of the proposed method is verified by a simulation example.

It is well known that the Kalman filter is globally optimal for linear time-invariant systems excited with white Gaussian noise along the process and measurement channels. However, its application to practical situations is often suboptimal because the noise covariance matrices typically are not accurately known. This paper presents a new covariance matching Kalman filter (CMKF) algorithm which estimates the measurement (R) or the process (Q) noise covariance matrix in addition to the state. The convergence of the filter for estimating Q or R matrices respectively is proved for discrete stochastic linear time-invariant systems under relatively mild conditions of observability.

The anisotropic norm of the linear discrete time invariant system is the measure of the system output sensitivity to a random input with the mean anisotropy bounded by some nonnegative value a. The mean anisotropy characterizes the degree of predictability of the stochastic signal. The anisotropic norm of a system is the induced norm with the extreme cases of H2 norm and H∞ norm, respectively, under a → 0 and a → ∞. The lower bound of the anisotropic norm of the linear discrete time invariant system was established in the present paper using the methods of linear algebra.

There is a well-developed theory describing inherent design limitations for linear time invariant feedback systems consisting of an analogue plant and analogue controller. This theory describes limitations on achievable performance present when the plant has non-minimum phase zeros, unstable poles, and/or time delays. The parallel theory for linear time invariant discrete time systems is less interesting because it describes system behaviour only at sampling instants. This paper develops a theory of design limitations for sampled-data feedback systems wherein the response of the analogue system output is considered. This is done using the fact that the steady-state response of a hybrid feedback system to a sinusoidal input consists of a fundamental component at the frequency of the input together with infinitely many harmonics at frequencies spaced integer multiples of the sampling frequency away from the fundamental. This fact allows fundamental sensitivity and complementary sensitivity functions that re...

The authors present an algorithm for order formulation of linear time invariant discrete systems using a new version of evolutionary computing technique namely, modified particle swarm optimization (MPSO). In the modified PSO, the movement of a particle is governed by three behaviors namely, inertia, cognitive and social. The cognitive behavior helps the particle to remember its previous visited best position. This paper proposes to split the cognitive behavior into two sections. This modification helps the model order formulation with minimum integral squared error. The results are shown in the form of unit step and unit impulse time response curves and compared with Genetic algorithm and general PSO based optimization techniques. The proposed method is illustrated through numerical example from literature.

This paper analyzes the effect of replay attacks on a control system. We assume an attacker wishes to disrupt the operation of a control system in steady state. In order to inject an exogenous control input without being detected the attacker will hijack the sensors, observe and record their readings for a certain amount of time and repeat them afterwards while carrying out his attack. This is a very common and natural attack (we have seen numerous times intruders recording and replaying security videos while performing their attack undisturbed) for an attacker who does not know the dynamics of the system but is aware of the fact that the system itself is expected to be in steady state for the duration of the attack. We assume the control system to be a discrete time linear time invariant gaussian system applying an infinite horizon Linear Quadratic Gaussian (LQG) controller. We also assume that the system is equipped with a ¿ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> failure detector. The main contributions of the paper, beyond the novelty of the problem formulation, consist in 1. providing conditions on the feasibility of the replay attack on the aforementioned system and 2. proposing a countermeasure that guarantees a desired probability of detection (with a fixed false alarm rate) by trading off either detection delay or LQG performance, either by decreasing control accuracy or increasing control effort.

Many different types of adaptive or universal controllers", capable of dealing with a very broad range of linear time-invariant systems, have been proposed. One class of such controllers uses switching between a finite, or at least countable, number of fixed controllers until stability is detected. Such controllers are very attractive from a theoretical viewpoint, in providing stabilization and asymptotic performance for a broad class of plants. However, such controllers are also known to have very poor transient properties, due to the long time required to search for a stabilizing feedback. The key contribution of this paper is to introduce the "method of localization" which can greatly improve the speed of the search. The method is described for linear time-invariant discrete time systems of known nominal order, with disturbances and noise present. Analysis and simulations demonstrate the potential for greatly improved transient performance.

Finite-time stability and stabilization of linear discrete time-varying stochastic systems

In this paper, we consider the analysis and synthesis problem for linear time-invariant distributed discrete time systems. These systems occur in many practical applications such as formation flight, control of systems described by partial differential equations, and control of automated vehicles moving in a platoon. Computationally attractive linear matrix inequality conditions are obtained for ensuring stability and induced /spl Lscr//sub 2/ performance. An example is given to motivate the class of systems we consider.

By the modem time series analysis method, based on the autoregressive moving average (ARMA) innovation models and white noise estimation theory, using the optimal fusion rule weighted by diagonal matrices, a distributed descriptor Wiener state fuser is presented by weighting the local Wiener state estimators for the linear discrete stochastic descriptor systems with multisensor. It realizes a decoupled fusion estimation for state components. In order to compute the optimal weights, the formulas of computing the cross-covariances among local estimation errors are presented based on cross-covariances among the local innovation processes, input white noise, and measurement white noises. It can handle the fused filtering, smoothing, and prediction problems in a unified framework. Its accuracy is higher than that of each local estimator. A Monte Carlo simulation example shows its effectiveness and correctness.

Reduced-order steady-state descriptor Kalman fuser weighted by block-diagonal matrices

Decoupled distributed Kalman fuser for descriptor systems

In this article, the problem of nonfragile finite-time stabilization for linear discrete mean-field stochastic systems is studied. The uncertain characteristics in control parameters are assumed to be random satisfying the Bernoulli distribution. A new approach called the “state-transition matrix method” is introduced and some necessary and sufficient conditions are derived to solve the underlying stabilization problem. The Lyapunov theorem based on the state-transition matrix also makes a contribution to the discrete finite-time control theory. One practical example is provided to validate the effectiveness of the newly proposed control strategy.

: This report considers a feedback control law for linear time-varying and time invariant discrete systems based on a receding horizon concept applied to a minimum energy problem with fixed terminal constraints. The control law is shown to be asymptotically stable and to result in a new method for stabilizing linear time-varying systems as well as extending some well known methods for stabilizing time invariant systems. In particular, the stabilizing gains of the feedback control law are obtained from the solution to a discrete Riccati equation over an arbitrary finite time interval, which is relatively easy to compute. The gain matrix reduces to a constant matrix for linear time invariant systems. Some stability results will turn out to be special cases of these results. The results parallel those for linear continuous time systems, although the technical details are tedious and more involved.