Random Transmission Delays Research Articles

Fault detection for a class of non‐linear networked control systems with data drift

In this paper, the fault detection problem is studied for a class of non-linear discrete-time networked control systems (NCSs). An individual stochastic variable satisfying a certain probabilistic distribution is utilised to describe the data drift of each sensor. The random transmission delays with the upper bound and the data drift phenomena are taken into account in a unified framework. By augmenting the states of the original non-linear NCS and the constructed full-order fault detection filter, the resulting fault detection dynamics is converted into an H ∞ filtering problem of a non-linear time-delay system. A sufficient condition for the existence of the designed fault detection filter is given in terms of a feasible linear matrix inequality, guaranteeing that the fault detection dynamics is stochastically stable and attains the prescribed H ∞ attenuation level. Finally, a numerical example is presented to show the effectiveness of the proposed method.

Feedback channel in linear noiseless dynamic systems controlled over the packet erasure network

This paper is concerned with tracking state trajectory at remote controller, stability and performance of linear time-invariant noiseless dynamic systems with multiple observations over the packet erasure network subject to random packet dropout and transmission delay that does not necessarily use feedback channel full time. Three cases are considered in this paper: (1) without feedback channel, (2) with feedback channel intermittently and (3) with full time availability of feedback channel. For all three cases, coding strategies that result in reliable tracking of state trajectory at remote controller with asymptotically zero mean absolute estimation error are presented. Asymptotic mean absolute stability of the controlled system equipped with each of these coding strategies is shown; trade-offs between duty cycle for feedback channel use, transmission delay and performance, which is defined in terms of the settling time, are studied.

Reliable H∞ Control for a Class of Nonlinear Networked Control Systems with Random Delays

AbstractIn this paper, the problem of reliable H∞ controller design is studied for a class of nonlinear networked control systems. A novel model is presented, which contains random transmission delays, faults of the sensor and actuator. The sensor‐to‐controller and controller‐to‐actuator transmission delays with upper bounds are considered, simultaneously. The working conditions of the sensor and actuator are formulated as two independent Markov chains, which take matrix values in finite sets, respectively. The resulting closed‐loop system is converted into a Markov switching system. On the basis of the cone complementary linearization algorithm, a mode‐dependent reliable controller is constructed such that the closed‐loop system is stochastically stable and attains the prescribed H∞ disturbance attenuation level. Finally, a numerical example is given to show the effectiveness of the developed technique.

Modeling and estimation for networked systems with multiple random transmission delays and packet losses

In networked systems, data packets are transmitted through networks from a sensor to a data processing center. Due to the unreliability of communication channels, a packet may be delayed even lost during the transmission. At each moment, the data processing center may receive one or multiple data packets or nothing at all. A novel model is developed to describe the possible multiple random transmission delays and data packet losses by employing a group of Bernoulli distributed random variables. It is transformed to a measurement model with multiple random delayed states and noises. Based on the model, an optimal linear filter in the linear minimum variance sense is proposed by using the orthogonal projection approach which is a universal tool to find the optimal linear estimate. It does not have a steady-state performance since it depends on the values of random variables that depict the phenomena of delays and losses at each moment. So it needs to be computed online. To reduce the online computational cost, a suboptimal linear filter dependent on the probabilities of random variables is also proposed. However, it is worth noting that it is linearly optimal among all the linear filters dependent on the probabilities. It can be computed offline since it has the steady-state performance. A sufficient condition of existence for the steady-state performance is given. A simulation example shows the effectiveness.

MixedH2/H∞control for a class of nonlinear discrete-time networked control systems with random delays and stochastic packet dropouts

The paper studies the problem of mixed H2/H∞ control for a class of nonlinear discrete-time networked control systems. By using the indicator function method, random network-induced delays and stochastic packet dropouts are taken into account in a unified framework in the designed mixed H2/H∞ controller. In the presences of random transmission delays, stochastic packet dropouts and all admissible disturbances, the resulting closed-loop system is stochastically stable in mean square and attains the prescribed H2 and H∞ performances. The designed mixed H2/H∞ controller can be obtained by solving a set of feasible linear matrix inequalities. Finally, a numerical example is provided to show the usefulness and effectiveness of the developed method. Copyright © 2014 John Wiley & Sons, Ltd.

Fault detection for a class of nonlinear networked control systems with Markov sensors assignment and random transmission delays

The paper investigates the fault detection problem for a class of nonlinear networked control systems with both communication constraints and random transmission delays. The access status of the sensors is governed by a stochastic event, which is modeled as a Markov chain taking matrix values in a certain set. The main task of this paper is to design a mode-dependent fault detection filter, such that for Markov sensors assignment, random network-induced delays and the unknown input signal, the error between the fault and the residual signal is minimized. And the resulting fault detection dynamics is formulated as an H∞ filtering problem of a Markov jump system. The linear matrix inequality-based sufficient conditions for the existence of the fault detection filter are obtained. Finally, two examples are given to show the effectiveness of the developed method.

Distributed Fusion Estimation With Missing Measurements, Random Transmission Delays and Packet Dropouts

This technical note is concerned with the distributed Kalman filtering problem for a class of networked multi-sensor fusion systems (NMFSs) with missing sensor measurements, random transmission delays and packet dropouts. A novel stochastic model is proposed to describe the transmission delays and packet dropouts, and an optimal distributed fusion Kalman filter (DFKF) is designed based on the optimal fusion criterion weighted by matrices. Some sufficient conditions are derived such that the MSE of the designed DFKF is bounded or convergent. Moreover, steady-state DFKF is also presented for the NMFSs. An illustrative example is given to demonstrate the effectiveness of the proposed results.

Performance Improved Methods for Communication-Based Train Control Systems With Random Packet Drops

Communication-based train control (CBTC) systems use wireless local area networks (WLANs) to transmit train status and control commands. Since WLANs are not originally designed for applications with high mobility, random transmission delays and packet drops are inevitable, which could result in unnecessary traction, brakes or even emergency brakes of trains, loss of line capacity, and passenger satisfaction. In this paper, we study the packet drops introduced by random transmission errors and handovers in CBTC systems, analyze the impact of random packet drops on the stability and performances of CBTC systems, and propose two novel schemes to improve the performances of CBTC systems. Unlike the existing works that only consider a single train and study the communication issues and train control issues separately, we model the system to control a group of trains as a networked control system (NCS) with packet drops in transmissions. Extensive field test and simulation results are presented. We show that our proposed schemes can provide less energy consumption, better riding comfortability, and higher line capacity compared with the existing scheme.

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

In networked control systems, random delays and packet dropouts are inevitable during data transmissions due to the limited communication capacity. The phenomena of random delays and packet dropouts of both sides from a sensor to an estimator and from a controller to an actuator are modeled via employing two groups of Bernoulli random variables. By defining some new variables, the original system with random delays and packet dropouts is equivalently transformed into a stochastic parameterized system. The optimal linear filter, predictor and smoother in the linear minimum variance sense are presented via the orthogonality projection approach. They depend on the probabilities of the stochastic parameters. The solutions to the optimal linear estimators are given by three equations including a Riccati, a Lyapunov and a simple difference. The stability of the proposed estimators is analyzed. At last, a sufficient condition for the existence of the steady-state estimators is given for time-invariant systems. Two examples are provided to verify the effectiveness of the proposed algorithms.

Variance-Constrained Robust Estimation for Discrete-Time Systems with Communication Constraints

This paper is concerned with a new filtering problem in networked control systems (NCSs) subject to limited communication capacity, which includes measurement quantization, random transmission delay, and packets loss. The measurements are first quantized via a logarithmic quantizer and then transmitted through a digital communication network with random delay and packet loss. The three communication constraints phenomena which can be seen as a class of uncertainties are formulated by a stochastic parameter uncertainty system. The purpose of the paper is to design a linear filter such that, for all the communication constraints, the error state of the filtering process is mean square bounded and the steady-state variance of the estimation error for each state is not more than the individual prescribed upper bound. It is shown that the desired filtering can effectively be solved if there are positive definite solutions to a couple of algebraic Riccati-like inequalities or linear matrix inequalities. Finally, an illustrative numerical example is presented to demonstrate the effectiveness and flexibility of the proposed design approach.

Optimal filtering for networked systems with Markovian communication delays

This paper is concerned with optimal filter problems for networked systems with random transmission delays, while the delay process is modeled as a multi-state Markov chain. By defining a delay-free observation sequence, the optimal filter problems are transformed into ones of the Markov jumping parameter system. We first present an optimal Kalman filter, which is with time-varying, path-dependent filter gains, and the number of the paths grows exponentially in time delay. Thus an alternative optimal Markov jump linear filter is presented, in which the filter gains just depend on the present value of the Markov chain. Further, an optimal filter with constant-gains is developed, the existence condition for the stabilizing solutions to the filter is given, and it can be shown that the proposed Markov jump linear filter converges to the constant-gain filter under appropriate assumptions.

Predictive Function Control for Communication-Based Train Control (CBTC) Systems

In Communication-Based Train Control (CBTC) systems, random transmission delays and packet drops are inevitable in the wireless networks, which could result in unnecessary traction, brakes or even emergency brakes of trains, losses of line capacity and passenger dissatisfaction. This paper applies predictive function control technology with a mixed H2 /∞ control approach to improve the control performances. The controller is in the state feedback form and satisfies the requirement of quadratic input and state constraints. A linear matrix inequality (LMI) approach is developed to solve the control problem. The proposed method attenuates disturbances by incorporating H2 /∞ into the control scheme. The control command from the automatic train operation (ATO) is included in the reward function to optimize the train's running profile. The influence of transmission delays and packet drops is alleviated through improving the performances of the controller. Simulation results show that the method is effective to improve the performances and robustness of CBTC systems.

Event-based LQG Control over Networks with Random Transmission Delays and Packet Losses

In Networked Control Systems (NCS), data networks not only limit the amount of information exchanged by system components but are also subject to stochastic packet delays and losses. In this paper, we present a controller that simultaneously addresses these problems by combining event-based and sequence-based control methods. At every time step, the proposed controller calculates a sequence of predicted control inputs and based on the expected future LQG costs decides whether it transmits the control sequence to the actuator. The proposed controller is evaluated with simulations.

Robust H∞ Control for Networked Systems with Random Packet Dropouts and Time Delays

This paper is concerned with the robust H∞ control problem for a class of networked systems with random transmission delays and packet dropouts. Both the sensor-to-estimator channel and the controller-to-actuator channel are considered. The random one-step transmission delays and packet dropouts are modeled by a Bernoulli distributed stochastic variable. Applied the linear matrix inequality (LMI) approach, an observer-based feedback controller is designed to make the closed-loop networked system to be robustly exponentially stable in the sense of mean square and the prescribed H∞ disturbance-rejection-attenuation level is also achieved. A simulation example is given to illustrate the proposed method.

H ∞ Control of Piecewise-Linear Systems Under Unreliable Communication Links

This paper considers the problem of H ∞ control of piecewise-linear control systems under unreliable communication links. Due to the limited bandwidth of the channels, signal transmission delays and data packet losses can occur between the plant and the controller. In the presence of random signal transmission delays and data packet losses, a piecewise controller is designed to stabilize the piecewise-linear system in the sense of mean square and also achieve a prescribed H ∞ disturbance attenuation performance based on piecewise-quadratic Lyapunov–Krasovskii functionals. It is shown that the H ∞ controllers can be designed by solving a set of linear matrix inequalities (LMIs) that are numerically feasible. Moreover, the controller design method is further extended to uncertain case where the system matrices’ uncertainties are represented in polytopic frameworks. Finally, an example is provided to illustrate the effectiveness of the developed theoretical results.

Filtering for networked control systems with single/multiple measurement packets subject to multiple-step measurement delays and multiple packet dropouts

The minimum-variance filtering problem in networked control systems, where both random measurement transmission delays and packet dropouts may occur, is investigated in this article. Instead of following the many existing results that solve the problem by using probabilistic approaches based on the probabilities of the uncertainties occurring between the sensor and the filter, we propose a non-probabilistic approach by time-stamping the measurement packets. Both single-measurement and multiple measurement packets are studied. We also consider the case of burst arrivals, where more than one packet may arrive between the receiver's previous and current sampling times; the scenario where the control input is non-zero and subject to delays and packet dropouts is examined as well. It is shown that, in such a situation, the optimal state estimate would generally be dependent on the possible control input. Simulations are presented to demonstrate the performance of the various proposed filters.

LQG Control for Networked Control Systems with Random Packet Delays and Dropouts via Multiple Predictive-Input Control Packets

This article addresses the Linear Quadratic Gaussian (LQG) optimal control problem for networked control systems when data is transmitted through a TCP-like network and both measurement and control packets are subject to random transmission delays and packet dropouts. Instead of adopting a “zero-input” or “hold-input” strategy, we propose a “predictive optimal-input” strategy, where at each time instant, K future control inputs are computed and sent in addition to the current one in the same control packet. The stabilizability conditions of the system are then derived. Simulation results are presented to demonstrate the effectiveness of the proposed approach.

Robust estimation for discrete time‐varying systems with limited communication capacity

AbstractIn this paper, we consider the state estimation problem for linear discrete time‐varying systems subject to limited communication capacity which includes measurement quantization, random transmission delay and data‐packet dropouts. Based on transforming the three communication limitations into the system with norm‐bounded uncertainties and stochastic matrices, we design a robust filter such that, for all the communication limitations, the error state of the filtering process is mean square bounded. An upper bound on the variance of the state estimation error is first found, and then, a robust filter is derived by minimizing the prescribed upper bound in the sense of the matrix norm. It is shown that the desired filter can be obtained in terms of the solutions to two Riccati‐like difference equations which also provide a recursive algorithm suitable for online computation. A simulation example is presented to demonstrate the effectiveness and applicability of the proposed algorithm.Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

Formation of synchronous activity through STDP in recurrent neural networks with heterogenous delays

The Spike-Timing Dependent Plasticity (STDP) rule originates from biological evidence [1] showing that an excitatory synapse is potentiated if the EPSP (Excitatory PostSynaptic Potential) is shortly followed by the emission of an action potential at the soma, and depressed in the opposite case (when the AP is followed by the EPSP). We study the effects of STDP on random recurrent network of spiking neurons of randomly coupled elements, with random axonal transmission delays, and no external input or additional noise. The initial activity is highly irregular (Figure 1, left). After applying Spike-Timing Dependent Plasticity for a long enough time (15–50 s), the activity before periodic and synchronized (Figure 1, right).

Robust stability conditions for remote SISO DMC controller in networked control systems

A two level hierarchy is employed in the design of networked control systems (NCSs) with bounded random transmission delay. At the lower level a local controller is designed to stabilize the plant. At the higher level a remote controller with the dynamic matrix control (DMC) algorithm is implemented to regulate the desirable set-point for the local controller. The conventional DMC algorithm is not applicable due to the unknown transmission delay in NCSs. To meet the requirements of a networked environment, a new remote DMC controller is proposed in this study. Two methods, maximum delayed output feedback and multi-rate sampling, are used to cope with the delayed feedback sensory data. Under the assumption that the closed-loop local system is described by one FIR model of an FIR model family, the robust stability problem of the remote DMC controller is investigated. Applying Jury’s dominant coefficient lemma and some stability results of switching discrete-time systems with multiple delays; several stability criteria are obtained in the form of simple inequalities. Finally, some numerical simulations are given to demonstrate the theoretical results.