Optimal estimation for systems with multiplicative noises, random delays and multiple packet dropouts

This article is concerned with the optimal linear estimation problem for linear discrete-time stochastic systems with possible multiple random measurement delays and packet dropouts, where the largest random delay is limited within a known bound and packet dropouts can be infinite. A new model is constructed to describe the phenomena of multiple random delays and packet dropouts by employing some random variables of Bernoulli distribution. By state augmentation, the system with random delays and packet dropouts is transferred to a system with random parameters. Based on the new model, the least mean square optimal linear estimators including filter, predictor and smoother are easily obtained via an innovation analysis approach. The estimators are recursively computed in terms of the solutions of a Riccati difference equation and a Lyapunov difference equation. A sufficient condition for the existence of the steady-state estimators is given. An example shows the effectiveness of the proposed algorithms.

This paper is concerned with the control problem for a class of systems with random delays and packet dropouts which unavoidably occur during the data transmission in the network. A novel model is developed to describe the random one-step delays and multiple packet dropouts from sensors to controllers and from controllers to actuators by applying four Bernoulli distributed stochastic variables. An observer-based feedback controller is designed via a linear matrix inequality (LMI) approach which guarantees the closed-loop networked system to be exponentially stable in the sense of mean square and also achieves the prescribed H ∞ disturbance-rejection-attenuation level. A simulation example shows the effectiveness of the proposed algorithm.

This paper studies the model reference H ∞ tracking control problem of networked control systems (NCSs) with random packet dropout in controller-to-actuator channels. A general packet dropout model in multiple channels case is adopted to formulate the information missing in the communication networks. The multiple channel packet dropout model results in complexities and difficulties in the tracking controller design. A latest received data dependent Lyapunov function is proposed and exploited to develop a sufficient condition for the H ∞ tracking controller design in terms of a linear matrix inequality (LMI). The proposed controller design method can guarantee asymptotic tracking of prescribed reference outputs while rejecting disturbances in mean square sense. A numerical example is given to illustrate the effectiveness of the proposed tracking controller design method.

This research is devoted to Fornasnisi-Marchesini model (FM). More precisely, the investigation of the control problem for the second model discrete-time FM. The model takes into account the random packet loss and quantization errors in the network environment. So our modelling method has the potential to achieve a better stabilization effects. Random packet dropouts, time delays and quantization are taken into consideration in the feedback control problem simultaneously. Measured signals are quantized before being communicated. A logarithmic quantizer is utilized and quantized signal measurements are handled by a sector bound method. The random packet dropouts are modeled as a Bernoulli process. A control law model which depends on packet dropouts and quantization is formulated. Notably, we lighten the assumptions by using the Schur complement. Besides, both a state feedback controller and an observer-based output feedback controller are designed to ensure corresponding closed-loop systems asymptotically stability. Sufficient conditions on mean square asymptotic stability in terms of LMIs have been obtained. Finally, two numerical example show the feasibility of our theoretical results.

This paper is concerned with the optimal and suboptimal deconvolution problems for discrete-time systems with random delayed observations. When the random delay is known online, i.e., time stamped, the random delayed system is reconstructed as an equivalent delay-free one by using measurement reorganization technique, and then an optimal input white noise estimator is presented based on the stochastic Kalman filtering theory. However, the optimal white-noise estimator is time- varying, stochastic, and doesn't converge to a steady state in general. Then an alternative suboptimal input white-noise estimator with deterministic gains is developed under a new criteria. The estimator gain and its respective error covariance-matrix information are derived based on a new suboptimal state estimator. It can be shown that the suboptimal input white-noise estimator converges to a steady-state one under appropriate assumptions.

In this paper, a Gaussian recursive filter is proposed for nonlinear networked systems with synchronously correlated noises and one-step randomly delayed measurements and multiple packet dropouts. Since each packet at the sensor side is sent only once and the system has one-step delay and multiple packet dropouts, the data processing center may receive zero/one/two measurements. By augmenting the system state at last epoch to the current one, employing two Bernoulli distributed random variables to describe the phenomena of delay and packet dropouts and using the prediction compensation mechanism, a novel model is derived. At the same time, to deal with the problem of correlated noise, Gaussian approximation recursive filter (GASF) is used. Based on the above processing, a nonlinear Gaussian recursive filter and corresponding numerical implementation based on cubature Kalman filter (CKF) are given. Compared with the existing results in linear systems, the proposed algorithm is more general and has higher estimation accuracy in nonlinear systems. The simulation results show the effectiveness of the proposed algorithm.

Based on a regular, causal descriptor controlled plant, the fault detection for a class of descriptor systems with both multiple measurement and control packet dropouts is investigated. Two independent Bernoulli distributed white sequences are used to describe the multiple measurement and control packet dropouts. The problem of fault detection for networked systems can be formulated as an H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">¿</sub> filtering problem in terms of H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">¿</sub> theory. Then a fault detection filter which has a given H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">¿</sub> performance is designed. A sufficient condition for the existence of the filter is established by means of linear matrix inequalities. At last a numerical example shows the validity of the proposed method.

This paper is concerned with the design of networked multi-sensor fusion estimation system (NMFES). The Kalman filtering problem is considered for the NMFES with random observation delays, packet dropouts and missing measurements caused by sensor failures. For each observation subsystem, the sensor failure phenomenon is described by a Bernoulli distributed white sequence with a known conditional probability, and the packet dropout phenomenon and randomly delayed measurements are described by multiple binary random variables. Without resorting to the augmentation technique, an optimal recursive fusion filter for NMFES is obtained in the linear minimum variance sense by using the innovation analysis method. The dimension of the designed filter is the same to the original system, which can help reduce computation costs as compared with the augmentation method. Moreover, the performance of the designed Kalman filter is dependent on the missing rates of the measurements, the upper bounds of random delays and the occurrence probabilities of delays. Finally, the effectiveness of the proposed results is demonstrated by an illustrative example.

SummaryThis note is concerned with the linear estimation problems for discrete‐time systems where the measurements are subject to random time delay and packet dropout. Different from most of previous works, the time‐stamping is assumed to be unavailable in this paper. In this case, the estimation problems for such systems are very difficult because the information of the received measurements is not exactly known in most cases. To overcome the difficulty caused by the random delay and unavailability of time‐stamping, a new observation is introduced by the summation of all the measurements received in the same time. Then, the random time delay measurement system is converted into a constant‐delay measurement system with multiplicative noises where the noise is binary distributed random variables with known distributions. Finally, the linear optimal estimator is derived by using the transformation of auto‐regressive moving average model to state‐space model and the standard Kalman filtering. The convergence and stability of the filter are also analyzed. A simulation example is given to show the effectiveness of the proposed estimator. Copyright © 2016 John Wiley &amp; Sons, Ltd.

In this paper, an H ∞ filter design problem is studied for networked stochastic linear discrete-time systems with mixed uncertainties of random measurement delays, packet dropouts and missing measurements. We model the packet delivery characteristics of the network as a four-state Markov process and note that the results for discrete-time linear systems with Markovian jumping parameters can be applied. We focus on the design problem of a full-order H ∞ filter such that for all possible uncertain measurements the filtering error dynamics is exponentially mean square stable and a prescribed H ∞ performance bound is guaranteed. Necessary and sufficient bilinear matrix inequality (BMI) condition for the synthesis of the aforementioned filter for a discrete-time jump system is presented. Some simulation examples are presented to show the applicability and effectiveness of the proposed approach.

Linear estimation for networked control systems with random transmission delays and packet dropouts

This note is concerned with the linear estimation problems for discrete-time systems where the measurements are subject to random time delay and packet drop. Due to the time stamping being assumed to be unavailable in this paper, the estimation problems for such systems are very difficult because the information of the received measurements is not exactly known in most cases. To overcome the difficulty caused by the random delay and unavailability of time-stamping, a new observation is defined by the summation of all the measurements received in the same time. Then the random time delay measurement system is converted into a constant-delay measurement system with multiplicative noises by using binary distributed random variables with known distributions. Finally, the linear optimal estimator is derived by combining the transformation of ARMA model to state-space model and the standard Kalman filtering. A simulation example is given to show the effectiveness of the proposed estimator.

In this note,Kalman filtering for systems with multiple packet dropouts is introduced. The random multiple packet dropouts are assumed to subject to the Bernoulli random binary distribution. A Kalman filter based on the white, zero-mean, correlated noises is proposed to design. And the stability of the designed filter is analyzed in this paper. Finally, a numerical example is exploited to show the usefulness of the proposed filter.

The control problem for the networked suspension control system of maglev train with random induced time delay and packet dropouts is investigated. First, Takagi-Sugeno (T-S) fuzzy models are utilized to represent the discrete-time nonlinear networked suspension control system, and the parameters uncertainties of the nonlinear model have also been taken into account. The controllers take the form of parallel distributed compensation. Then, a sufficient condition for the stability of the networked suspension control system is derived. Based on the criteria, the state feedback fuzzy controllers are obtained, and the controller gains can be computed by using MATLAB LMI Toolbox directly. Finally, both the numerical simulations and physical experiments on the full-scale single bogie of CMS-04 maglev train have been accomplished to demonstrate the effectiveness of this proposed method.

This study is concerned with the linear estimation problem for networked systems with one‐step random delay and multiple packet dropouts. At each moment, the estimator may receive one or two data packets or nothing. The predictor of sensor measurement at the current instant is used as a compensator if the current measurement does not arrive at the estimator. Based on the developed compensation model, the optimal linear estimators including filter, predictor and smoother are proposed by the innovation analysis approach. Compared with the estimators based on the compensation of using the latest measurement previously received in the existing literatures, the proposed estimators have higher estimation accuracy and smaller computational burden. Simulation results show the effectiveness of the proposed algorithms.