Random Transmission Delays Research Articles

Optimal sequential fusion estimation for sampled‐data systems with random delays and multiplicative noise

AbstractThis article is concerned with the optimal sequential fusion filter design issue for a class of sampled‐data systems subject to random transmission delays and multiplicative noise. The considered delay is modeled as a multistate Markov chain, while the multiplicative noise corrupting the observation measurements is assumed be a white noise sequence with known statistical properties. First, by reorganizing the original measurements, the solvability of the addressed problem is cast into the feasibility of an optimal estimation issue for the hybrid Markovian jump system without delays. Then, an optimal sequential fusion filter is constructed by utilizing a dynamic model with finite jumps on basis of the arrival order of measurements from different sensors, guaranteeing estimation performances both at sampling instants and within the sampling intervals. Moreover, the desired estimator gains can be computed via solving a series of coupled differential Riccati equations with jumps and coupled differential Lyapunov equations. Further, a stationary sequential fusion filter is achieved with the guarantee of the exponentially mean‐square stability. Finally, two simulation examples are provided to verify the validity of the proposed algorithms.

Cooperative target estimation of strap-down missiles considering random measurement delay

Aiming at the problem of cooperative target estimation for multiple strap-down missiles, this paper is concerned with developing a distributed cooperative estimation fusion algorithm considering the random transmission delay of observation data. As a stepping stone, the random measurement delay system with multiple strap-down missiles is transformed into a delay-free system with correlation noise in finite time intervals using the random observation delay model for strap-down missiles. Then, the distributed fusion technique without feedback is proposed based on the design of the best local filter for each strap-down sampling subsystem; To further enhance the robustness and stability of the cooperative target estimation system, the distributed fusion algorithm with feedback is suggested. Simulation in various cases and comparison studies are conducted to verify the effectiveness and robustness of the proposed scheme.

Multi-sensor information fusion filtering for delayed nonlinear stochastic singular systems with packet disorders

The fusion filtering problem is investigated for a class of time-varying nonlinear singular systems with packet disorders (PDs). The key idea is to transfer the original singular systems with multiple sensors to full-order augmented nonsingular systems by utilizing the matrix transformation method. The phenomenon of PDs accompanied with random transmission delays (RTDs) is considered, which exists in the channel from sensor to filter. A set of independent and identically distributed random variables obeying known probability distribution are introduced to model the RTDs. A centralized fusion filter is designed, which employs the rounding function of the mathematical expectation of the RTDs. Furthermore, the nonlinear function is linearized by utilizing the method of Taylor series expansion. Then, the desired upper bounds of the estimation error covariance are guaranteed and then locally minimized through appropriately designing the corresponding filter gains. Finally, a numerical example with comparisons is carried out to verify the feasibility of the proposed fusion filtering method.

An event‐triggered method to distributed filtering for nonlinear multi‐rate systems with random transmission delays

SummaryIn this article, an event‐triggered recursive filtering problem is studied for a class of nonlinear multi‐rate systems (MRSs) with random transmission delays (RTDs). The RTDs are described by utilizing random variables with a known probability distribution and the Kronecker function. To facilitate further study, the MRS is converted into a single‐rate one by adopting an iteration equation approach. To address the challenge of filter design caused by different measurement sampling periods, a modified prediction method of measurements is given. Moreover, an event‐triggered mechanism (ETM) is introduced to regulate the innovation transmission frequency. The objective of the addressed filtering problem is to design a recursive distributed filtering method for MRSs subject to ETM and RTDs, where a minimum upper bound on the filter error covariance is obtained. Moreover, the filter gain matrix is formulated by resorting to the solutions to matrix difference equations. Besides, the boundedness in the mean‐square sense of the filtering error is analyzed and a sufficient condition is provided. Finally, simulations with comparison experiments are presented to demonstrate the effectiveness of the newly proposed theoretical results.

Stability Analysis and Synthesis for Networked Systems With Noisy Sampling Intervals, Random Transmission Delays, and Packet Dropouts

In this article, we study the stability analysis and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> controller synthesis problems for networked systems with random transmission delays and packet dropouts that are subject to noisy sampling intervals. The sampling errors and transmission delays are described by an independent and identically distributed sequence of continuous random variables and the transmission delays are assumed to be smaller than the noisy sampling intervals. First, a closed-loop discrete-time stochastic framework for networked system that allows investigating noisy sampling intervals, random transmission delays and packet dropouts simultaneously is established. To render the discrete-time stochastic system suitable for stability analysis and synthesis, an equivalent yet tractable stochastic augmented model is then reformulated with the help of matrix exponential computation. Based on this augmented model, a stability condition involving the expectation of a nonlinear and random coupling matrix is derived. By recurring to the law of total expectation and Kronecker product operation, the expectation operation of the coupling matrix subject to high nonlinearity and multiple randomness is decoupled. Subsequently, a controller algorithm is designed such that the exponential mean-square stability of the original discrete-time stochastic system with a prescribed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> performance is guaranteed. Finally, an example is provided to illustrate the effectiveness of the controller design algorithm.

Disorder-resistant fusion estimator design for nonlinear stochastic systems in the presence of measurement quantization

In this paper, we thoroughly study a new nonlinear disorder-resistant fusion estimation problem under both packet disorder and measurement quantization. Packet disorder, which occurs due mainly to random transmission delays (RTDs), are characterized via a series of integer-valued functions and random variables obeying certain distributions. Sensor measurements are logarithmically quantized before entering designated communication networks. The upper bounds on the filtering error covariances are acquired and later minimized by appropriately designing gain parameters of both local and fusion estimators. For fusion estimation, all local estimates and filtering covariances are integrated at a fusion center through the well-known federated criterion. Moreover, the fusion performance is examined by means of assessing the resistance of the designed estimator against the RTD-induced disorder. Simulation examples are presented to illustrate the applicability of the proposed disorder-resistant fusion estimator.

Exponential mean-square stabilization control for cyber-physical systems under random DoS attacks and transmission delay

Exponential mean-square stabilization control for cyber-physical systems under random DoS attacks and transmission delay

Integrated Stabilizing Control for Sampled-Data NCSs With Intermittent Observation and Multiple Random Transmission Delays

In this paper, we study sampled-data networked control systems (NCSs) that operate over communication networks with multi-path channels. Due to limited bandwidth power, the delivery of observed state signals from the sensor to the controller may suffer packet loss possibility, which leads to intermittent observation. An unreliable multi-path routing network is responsible for the transmission of control signals from the controller to the actuator, subject to random transmission delays. These communication problems lead to degradation in system performance, which may even cause instability. By utilizing an idle-time-based scheduling policy with a pre-defined deadline constraint on the actuator side, we transform the affiliated integrated system into a stochastic model with constant input delay. For such implementation, we propose a set of Riccati-type stabilization conditions, which are necessary and sufficient. It is remarkable that the stabilizing control policy is designed based on the feedback of the optimal estimate with minimum mean square error. Moreover, for the scalar system, we study the uniqueness and existence property of the maximum sampling period, and derive its close form representation in terms of system parameters, service capability and packet dropout rate.

A pipelining task offloading strategy via delay-aware multi-agent reinforcement learning in Cybertwin-enabled 6G network

Cybertwin-enabled 6th Generation (6G) network is envisioned to support artificial intelligence-native management to meet changing demands of 6G applications. Multi-Agent Deep Reinforcement Learning (MADRL) technologies driven by Cybertwins have been proposed for adaptive task offloading strategies. However, the existence of random transmission delay between Cybertwin-driven agents and underlying networks is not considered in related works, which destroys the standard Markov property and increases the decision reaction time to reduce the task offloading strategy performance. In order to address this problem, we propose a pipelining task offloading method to lower the decision reaction time and model it as a delay-aware Markov Decision Process (MDP). Then, we design a delay-aware MADRL algorithm to minimize the weighted sum of task execution latency and energy consumption. Firstly, the state space is augmented using the lastly-received state and historical actions to rebuild the Markov property. Secondly, Gate Transformer-XL is introduced to capture historical actions' importance and maintain the consistent input dimension dynamically changed due to random transmission delays. Thirdly, a sampling method and a new loss function with the difference between the current and target state value and the difference between real state-action value and augmented state-action value are designed to obtain state transition trajectories close to the real ones. Numerical results demonstrate that the proposed methods is effective in reducing reaction time and improving the task offloading performance in the random-delay Cybertwin-enabled 6G networks.

Distributed optimal fusion filtering for singular systems with random transmission delays and packet dropout compensations

This paper is concerned with the fusion filtering problem for time-varying singular systems with random transmission delays (RTDs) and packet dropout (PD) compensations. Here, the phenomena of RTDs and PDs are both characterized by Bernoulli distributed random variables with different probabilities. Generally, the current sensor measurement and one-step delayed sensor measurement can be received by filter. When the sensor measurement is lost, based on the strategy of PD compensations, the one-step predictor of current sensor measurement is used as compensator. Then, the new augmented systems with stochastic parameter matrices and correlated noises are introduced based on the measurement compensation model. Utilizing the innovation analysis approach, the local filters (LFs) dependent on probabilities and corresponding estimation error covariance matrices are derived for augmented systems. Moreover, the matrix-weighted distributed fusion filter (DFF) is designed for original singular systems on the basis of the state transformation. Compared with the LFs, it is not difficult to see that the presented DFF has better precision. In the end, some comparison simulation experiments are carried out to verify the effectiveness of the proposed fusion filtering algorithm.

Probability-Density-Dependent Load Frequency Control of Power Systems With Random Delays and Cyber-Attacks via Circuital Implementation

This paper studies the decentralized <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> secure load frequency control issue and circuital realization of multi-area networked power systems subject to random transmission delays and deception attacks. To make full use of the stochastic feature of the network-induced transmission delay, its distribution described by the probability density function is utilized. Due to this feature, the normal control signal and the injected deceptive attack signal transmitted over the network can be formed as two distributed delay terms. Then, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$i$ </tex-math></inline-formula> th load frequency control area is established as a new distributed delay system, in which the delay probability density is treated as the distributed kernel. By utilizing an integral inequality dependent on the kernel, new sufficient controller design conditions are derived to guarantee the system stability with given <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> performance. Moreover, a physical execution approach is addressed to transfer the load frequency control systems into electrical analogy circuits. The effectiveness of the proposed approach is illustrated via the professional simcape toolbox in Simulink/MATLAB for circuit simulations.

Recursive distributed fusion estimation for multi-sensor systems with missing measurements, multiple random transmission delays and packet losses

This paper is concerned with the recursive distributed fusion estimation problems for networked multi-sensor systems with missing measurements, multiple random transmission delays, and packet losses. There exist missing measurements in the observation equations due to unpredictable sensor faults. Moreover, there are often random delays and losses during data transmissions from sensors to the fusion center due to limited communication bandwidths of the network. The Kalman-like recursive distributed fusion predictor and filter in the linear unbiased minimum variance (LUMV) sense are, respectively presented based on local estimates, cross-covariance matrices between local estimates, and cross-covariance matrices between the prior fusion estimate and local estimates. The stability and steady-state property of the proposed algorithms are analyzed. Their estimation accuracy is better than that of local estimates and distributed fusion estimates by matrix-weighting local estimates. A simulation example shows the effectiveness of the proposed algorithms.

Distributed Fusion Estimation for Stochastic Uncertain Systems With Network-Induced Complexity and Multiple Noise.

This article investigates an issue of distributed fusion estimation under network-induced complexity and stochastic parameter uncertainties. First, a novel signal selection method based on event trigger is developed to handle network-induced packet dropouts, as well as packet disorders resulting from random transmission delays, where the H2/H∞ performance of the system is analyzed in different noise environments. In addition, a linear delay compensation strategy is further employed for solving the complex network-induced problem, which may deteriorate system performance. Moreover, a weighted fusion scheme is used to integrate multiple resources through an error cross-covariance matrix. Several case studies validate the proposed algorithm and demonstrate satisfactory system performance in target tracking.

TACAN: The Shaping of Delay Distribution Under Multipath Fading Channel for Industrial IoT Systems

The wireless-enabled Industrial Internet of Things (IIoT) system is promising due to its flexibility and cable-free deployment. The varying fading channel will lead to the random transmission delays and jitters, which are the major challenges hindering the adoption of wireless communication in mission-critical industrial systems. The performance or even the stability of closed-loop feedback control system will degrade severely with such delays and jitters. As a result, the maximum delay margin should be met to guarantee the performance of the IIoT system. Aiming to better satisfy this requirement, a novel concept to shape the delay distribution under the industrial multipath fading channel is proposed in this article. Consequently, a two-layer closed feedback control algorithm, referred as TACAN in this article, is designed through the decoupling of original optimization function, by which the variance of the delay distribution is minimized to improve the reliability and stability of the IIoT systems. The performance of proposed delay shape control method is verified by both the classical Rician channel model and the field measured industrial fading channel responses.

Distributed filtering for time-varying state-saturated systems with packet disorders: An event-triggered case

This paper investigates the distributed filtering (DF) issue for a class of time-varying state-saturated systems with packet disorders (PDs) via the event-triggered communication mechanism (ETCM). The random transmission delays, which can be characterized by a set of random variables obeying certain probability distribution, cause the phenomenon of PDs. In addition, for the sake of decreasing the consumption of network resources, the ETCM is used to arrange the data transmission. On the basis of the measurable data information, a novel distributed filter is constructed that can ensure the existence of the upper bound matrix (UBM) regarding the filtering error (FE) covariance and then the trace of the presented UBM is minimized via constructing the suitable filter gain. Afterwards, the boundedness analysis of FE dynamics is provided to evaluate the filtering algorithm performance. Finally, the validity of the designed DF scheme is illustrated through a numerical experiment.

Optimal output feedback control of a class of linear systems with quasi-colored control-dependent multiplicative noise

This paper addresses the mean-square optimal control problem for a class of discrete-time linear systems with a quasi-colored control-dependent multiplicative noise via output feedback. The noise under study is novel and shown to have advantage on modeling a class of network phenomena such as random transmission delays. The optimal output feedback controller is designed using an optimal mean-square state feedback gain and two observer gains, which are determined by the mean-square stabilizing solution to a modified algebraic Riccati equation (MARE), provided that the plant is minimum-phase and left-invertible. A necessary and sufficient condition for the existence of the stabilizing solution to the MARE is explicitly presented. It shows that the separation principle holds in a certain sense for the optimal control design of the work. The result is also applied to the optimal control problems in networked systems with random transmission delays and analog erasure channels, respectively.

Recursive state estimation for a class of nonlinear uncertain coupled complex networks subject to random link failures and packet disorders

This paper is concerned with the recursive state estimation (RSE) problem under minimum mean-square error sense for a class of nonlinear complex networks (CNs) with uncertain inner coupling, random link failures and packet disorders. Firstly, a set of random variables obeying the Bernoulli distribution is adopted to characterize whether there are connections between different network units, i.e., there is no random link failure when the random variable is equal to 1, otherwise the random link failure occurs. In addition, the inner coupling strength is assumed to be varying within a given interval and the phenomenon of packet disorders caused by the random transmission delay (RTD) is also taken into account. In our study, the nonlinearity satisfies the continuously differentiable condition, which can be linearized by resorting to the Taylor expansion. The focus of the addressed RSE problem is on the design of an RSE approach in the mean-square error sense such that, for all uncertain inner coupling, random link failures and packet disorders, a suboptimal upper bound of the state estimation error covariance is obtained and minimized by parameterizing the state estimator gain with explicit expression form. Furthermore, a sufficient condition with respect to the uniform boundedness of state estimation error in mean-square sense is elaborated. Finally, a numerical experiment is introduced to demonstrate the validity of the presented RSE approach.

Real-Time nonlinear predictive controller design for drive-by-wire vehicle lateral stability with dynamic boundary conditions

Due to flexible drive-by-wire technology, vehicle stability control can improve handling and lateral stability under extreme conditions. However, this technology can also increase the probability of random transmission delay. This paper proposes a nonlinear model predictive control (NMPC) strategy to improve vehicle stability and compensate for the random time delay. First, by combining the nonlinear dynamic characteristics and driver behavior, we obtain a stable region of the yaw rate and the sideslip angle under complex driving conditions. Second, an NMPC controller is designed to track the reference values in the identified stable region to improve the handling and lateral stability. Finally, the actuator receives the optimized control sequence and compensates for the random time delay of the transmission channel. CarSim/Simulink simulation and hardware-in-the-loop experiment results show that the proposed controller with dynamic boundary conditions can better track the expected value of the yaw rate and suppress the sideslip angle under low adhesion road conditions.

Recursive State Estimation for Stochastic Complex Networks Under Round-Robin Communication Protocol: Handling Packet Disorders

This paper investigates the recursive state estimation problemfor a class of discrete-time stochastic complex networks with packet disorders under Round-Robin (RR) communication protocols. The phenomenon of packet disorders results from the random transmission delays during the signal propagation process due to the unpredictable fluctuations of the network load, and such random delays are modeled by a set of random variables satisfying certain known probability distributions. For the sake of lessening the communication burden and abating the data collisions, the RR protocol is introduced to govern the order of the nodes for data transmission. Under the scheduling of the RR protocol, only one node is allowed to gain the access to the network at each time instant. Then, a recursive estimator is devised to guarantee an upper bound for the estimation error covariance, and then the obtained upper bound is locally minimized by adequately choosing the estimator parameters. Furthermore, the boundedness of estimation error is analyzed in the sense of mean square with the help of stochastic analysis techniques. At last, a simulation example is presented to show the applicability of the proposed estimator design scheme.

Scalable event-triggered distributed extended Kalman filter for nonlinear systems subject to randomly delayed and lost measurements

In this paper, a distributed extended Kalman filter (EKF) is developed for a class of nonlinear systems, whose outputs are measured by multiple sensors which send data using an event triggered mechanism through a communication network subject to loss and latency. Random transmission delay and multiple dropouts are modelled by a Bernoulli random sequence. The filter gains are determined in each sensor node such that an upper bound on the cross covariance of the estimation error is minimized; so, less computational burden is required, even in the networks with the large number of nodes. To be specific, the scalability is the main feature of the proposed scheme. The boundedness of the filtering error is proved under some conditions. Finally, comparative simulation results are presented to illustrate the effectiveness and the applicability of the suggested filter.