Time Delay Probability Research Articles

Unknown input observer based distributed fault detection for nonlinear multi-agent systems with probabilistic time delay

This paper focuses on the fault detection (FD) problem for nonlinear continuous-time multi-agent systems (MASs) with external disturbances and random time-varying delay. The communication topology is assumed to be undirected and connected. Firstly, a stochastic variable satisfying the Bernoulli distribution is utilized to describe the random time-varying delay and transfer the random time-varying delay to a deterministic time-varying delay. To avoid the constraints of the rank conditions for unknown input observer (UIO), the external disturbances and faults from other agents are treated as the unknown inputs which are partitioned into the decoupled part and the non-decoupled part. Sufficient conditions composed of linear matrix inequalities (LMIs) are derived to ensure the stochastic stability of the augmented system with a desired H∞ performance index and extra freedom of design. By utilizing the properties of UIOs properly, the method proposed in this paper can detect multiple faulty nodes simultaneously. Finally, a numerical example demonstrates the effectiveness and feasibility of the proposed approach.

Extended Dissipativity Performance of High-Speed Train Including Actuator Faults and Probabilistic Time-Delays Under Resilient Reliable Control

The problem of extended dissipativity performance of a high-speed train (HST) with probabilistic delays and actuator faults under resilient reliable control has been exploited in this article. An extended dissipativity index is selected to perform a unified control design procedure for the HST dynamics, which is more general than (\mathbb Q,\mathbb S,\mathbb R)-dissipativity index. Specifically, a sequence of random variables responding the Bernoulli distribution is exploited to govern the probabilistic time-delays. By utilizing the tighter integral inequality (TII) and reciprocally convex inequality (RCI) technique, some criteria are launched in terms of the linear matrix inequalities (LMIs). Finally, simulations show the effectiveness and applicability of the offered control law by inspecting the Japan Shinkansen HST with its experimental values, along with a comparison study also been exploited to showing the merits and generalization of the proposed control design technique.

Optimal mean‐square consensus for heterogeneous multi‐agent system with probabilistic time delay

This paper studies the mean-square consensus for heterogeneous multi-agent systems with probabilistic time delay. Each agent in the system has an objective function and only knows its own objective function. Control protocols for the system both over the fixed and the switched weighted-balanced topologies are designed. The consensus state of agents' position can make the sum of objective functions minimum. By adopting probability statistics, stochastic process, matrix theory and some stability method, sufficient conditions for the consensus protocol are given. Several simulations are presented to illustrate the potential correctness of the results.

H ∞ state estimation for discrete memristive neural networks with signal quantization and probabilistic time delay

In this paper, the problem of state estimation is discussed for a class of delayed discrete memristive neural networks with signal quantization. A random variable obeying the Bernoulli distribution is used to describe the probabilistic time delay. A switching function is introduced to reflect the state dependence of memristive connection weight on neurons. Our aim is to design a state estimator to ensure that the specified disturbance attenuation level is guaranteed. By using Lyapunov stability theory and inequality scaling techniques, the specific explicit expression of gain parameter is given. Finally, a numerical example is given to verify the effectiveness of the proposed estimation method.

Mean-square consensus for heterogeneous multi-agent systems with probabilistic time delay

This paper studies the delay-dependent consensus problem of heterogeneous multi-agent systems over directed topology. The heterogeneous dynamics consisting of both first-order and second-order agents with random time delay are considered. New distributed control protocols based on the probability distribution of time delay are proposed for the leader-following and leaderless systems. By adopting matrix theory, Lyapunov-Krasovskii function and stochastic analysis, some less conservative conditions for the mean-square consensus are established over directed fixed topology and switching topologies. Moreover, the larger upper bounds of time delay are obtained. Finally, several simulations are presented to illustrate the obtained results.

Finite-Time Consensus of Finite Field Networks With Stochastic Time Delays

This brief aims to solve the finite-time consensus problem of finite field networks (FFNs) with stochastic time delays. An algebraic state space representation (ASSR) approach is introduced for the investigation of this problem. Firstly, the concept of finite-time consensus with probability one is defined for FFNs with two kinds of stochastic time delays. Secondly, the dynamics of FFNs with time delays is converted into an ASSR, based on which, the dynamics of FFNs with probabilistic time delay is converted into a linear discrete-time stochastic system. It is shown that the finite-time consensus of FFNs with probabilistic time delay is equivalent to the finite-time set stability of the obtained system. Thirdly, a verifiable criterion is put forward for the finite-time consensus of FFNs with probabilistic time delay. Finally, using the dummy matrix, the dynamics of FFNs with Markov jump time delay is also converted into a linear discrete-time stochastic system, and the corresponding criterion is proposed for the finite-time consensus of FFNs with Markov jump time delay.

Synchronization for discrete-time complex networks with probabilistic time delays

This paper investigates the problem of adaptive synchronization for discrete-time complex dynamical networks with random delays. In such complex systems, there occurs two kinds of nonidentical probability delays, i.e. self-feedback delays and coupling delays, and these delays are assumed to take values in a given finite sets with probability distributions. By means of the Lyapunov theory, discrete-time Jensen inequality and reciprocal convex combination approach, several delay-probability-distribution-dependent conditions are derived in the linear matrix inequality (LMI) format such that the discrete-time complex dynamical networks with random delays are globally synchronization in mean square. In addition, we use Watts–Strogatz (WS) random complex networks and regular Rulkov networks as two numerical examples to illustrate the effectiveness of our theoretical analysis.

Filtering and inference for stochastic oscillators with distributed delays.

MotivationThe time evolution of molecular species involved in biochemical reaction networks often arises from complex stochastic processes involving many species and reaction events. Inference for such systems is profoundly challenged by the relative sparseness of experimental data, as measurements are often limited to a small subset of the participating species measured at discrete time points. The need for model reduction can be realistically achieved for oscillatory dynamics resulting from negative translational and transcriptional feedback loops by the introduction of probabilistic time-delays. Although this approach yields a simplified model, inference is challenging and subject to ongoing research. The linear noise approximation (LNA) has recently been proposed to address such systems in stochastic form and will be exploited here.ResultsWe develop a novel filtering approach for the LNA in stochastic systems with distributed delays, which allows the parameter values and unobserved states of a stochastic negative feedback model to be inferred from univariate time-series data. The performance of the methods is tested for simulated data. Results are obtained for real data when the model is fitted to imaging data on Cry1, a key gene involved in the mammalian central circadian clock, observed via a luciferase reporter construct in a mouse suprachiasmatic nucleus.Availability and implementationProgrammes are written in MATLAB and Statistics Toolbox Release 2016 b, The MathWorks, Inc., Natick, Massachusetts, USA. Sample code and Cry1 data are available on GitHub https://github.com/scalderazzo/FLNADD.Supplementary information Supplementary data are available at Bioinformatics online.

Set stability and synchronization of logical networks with probabilistic time delays

Using the algebraic state space representation (ASSR) method, this paper investigates the set stability and synchronization of Boolean networks with probabilistic time delays (PTDs). Firstly, an equivalent stochastic system is established for the Boolean network with PTDs by using the ASSR method. Secondly, based on the probabilistic state transition matrix of equivalent stochastic system, a necessary and sufficient condition is proposed for the set stability of Boolean networks with PTDs. Thirdly, as an application of set stability, the synchronization of coupled Boolean networks with PTDs is studied, and a necessary and sufficient condition is presented. Finally, an illustrative example is given to demonstrate the effectiveness of the obtained new results.

Impulsive discrete-time GRNs with probabilistic time delays, distributed and leakage delays: an asymptotic stability issue

Impulsive discrete-time GRNs with probabilistic time delays, distributed and leakage delays: an asymptotic stability issue

Robust consensus of nonlinear multi‐agent systems via reliable control with probabilistic time delay

In this paper, the consensus problem of uncertain nonlinear multi‐agent systems is investigated via reliable control in the presence of probabilistic time‐varying delay. First, the communication topology among the agents is assumed to be directed and fixed. Second, by introducing a stochastic variable which satisfies Bernoulli distribution, the information of probabilistic time‐varying delay is equivalently transformed into the deterministic time‐varying delay with stochastic parameters. Third, by using Laplacian matrix properties, the consensus problem is converted into the conventional stability problem of the closed‐loop system. The main objective of this paper is to design a state feedback reliable controller such that for all admissible uncertainties as well as actuator failure cases, the resulting closed‐loop system is robustly stable in the sense of mean‐square. For this purpose, through construction of a suitable Lyapunov–Krasovskii functional containing four integral terms and utilization of Kronecker product properties along with the matrix inequality techniques, a new set of delay‐dependent consensus stabilizability conditions for the closed‐loop system is obtained. Based on these conditions, the desired reliable controller is designed in terms of linear matrix inequalities which can be easily solved by using any of the effective optimization algorithms. Moreover, a numerical example and its simulations are included to demonstrate the feasibility and effectiveness of the proposed control design scheme. © 2016 Wiley Periodicals, Inc. Complexity 21: 138–150, 2016

Reliable Mixed H∞ and Passivity-Based Control for Fuzzy Markovian Switching Systems With Probabilistic Time Delays and Actuator Failures.

This paper is concerned with the problem of reliable mixed H ∞ and passivity-based control for a class of stochastic Takagi-Sugeno (TS) fuzzy systems with Markovian switching and probabilistic time varying delays. Different from the existing works, the H∞ and passivity control problem with probabilistic occurrence of time-varying delays and actuator failures is considered in a unified framework, which is more general in some practical situations. The main aim of this paper is to design a reliable mixed H∞ and passivity-based controller such that the stochastic TS fuzzy system with Markovian switching is stochastically stable with a prescribed mixed H∞ and passivity performance level γ > 0 . Based on the Lyapunov-Krasovskii functional (LKF) involving lower and upper bound of probabilistic time delay and convex combination technique, a new set of delay-dependent sufficient condition in terms of linear matrix inequalities (LMIs) is established for obtaining the required result. Finally, a numerical example based on the modified truck-trailer model is given to demonstrate the effectiveness and applicability of the proposed design techniques.

Fault-tolerant sampled-data control of flexible spacecraft with probabilistic time delays

In this paper, fault-tolerant sampled-data control for flexible spacecraft in the presence of external disturbances, partial actuator failures and probabilistic time delays is investigated. In particular, unlike the common assumptions on continuous-time information on control input, a more realistic sampled-data communication strategy is proposed with probabilistic occurrence of time-varying delays which is modeled by introducing Bernoulli distributed sequences. The main purpose of this paper is to derive fault-tolerant sampled-data control law which makes the closed-loop system robustly asymptotically stable with a prescribed upper bound of the cost function about its equilibrium point for all possible actuator failures. More precisely, by constructing an appropriate Lyapunov–Krasovskii functional involving the lower and upper bound of the probabilistic time delay, a new set of sufficient conditions are derived in terms of linear matrix inequalities for achieving the required result. Numerical simulations are presented by taking the real parameters to the considered aircraft model, which is not only highlighting the ensured closed-loop performance by the proposed control law, but also illustrates its superior fault tolerance, fast convergence and robustness in the presence of external disturbances and actuator faults when compared with the conventional controller. The simulation result reveals the effectiveness and potential of the proposed new design techniques.

Consensus of Euler-Lagrange systems networked by sampled-data information with probabilistic time delays.

This paper investigates the consensus problem of multiple Euler-Lagrange systems under directed topology. Unlike the common assumptions on continuous-time information exchanges, a more realistic sampled-data communication strategy is proposed with probabilistic occurrence of time-varying delays. Both of the sampling period and the delays are assumed to be time-varying, which is more general in some practical situations. In addition, the relative coordinate derivative information is not required in the distributed controllers such that the communication network burden can be further reduced. In particular, a distinct feature of the proposed scheme lies in the fact that it can effectively reduce the energy consumption. By employing the stochastic analysis techniques, sufficient conditions are established to guarantee that the consensus can be achieved. Finally, a numerical example is provided to illustrate the applicability and benefits of the theoretical results.

Exact likelihood computation in Boolean networks with probabilistic time delays, and its application in signal network reconstruction

For biological pathways, it is common to measure a gene expression time series after various knockdowns of genes that are putatively involved in the process of interest. These interventional time-resolved data are most suitable for the elucidation of dynamic causal relationships in signaling networks. Even with this kind of data it is still a major and largely unsolved challenge to infer the topology and interaction logic of the underlying regulatory network. In this work, we present a novel model-based approach involving Boolean networks to reconstruct small to medium-sized regulatory networks. In particular, we solve the problem of exact likelihood computation in Boolean networks with probabilistic exponential time delays. Simulations demonstrate the high accuracy of our approach. We apply our method to data of Ivanova et al. (2006), where RNA interference knockdown experiments were used to build a network of the key regulatory genes governing mouse stem cell maintenance and differentiation. In contrast to previous analyses of that data set, our method can identify feedback loops and provides new insights into the interplay of some master regulators in embryonic stem cell development. The algorithm is implemented in the statistical language R. Code and documentation are available at Bioinformatics online. duemcke@mpipz.mpg.de or tresch@mpipz.mpg.de Supplementary Materials are available at Bioinfomatics online.

Robust stability analysis for discrete-time genetic regulatory networks with probabilistic time delays

This paper investigates the robust stability problem of a class of discrete-time genetic regulatory networks (GRNs) with probabilistic time delays. Different from the previous works, at each instant the feedback regulation delay and the translation delay are assumed to take values in two given finite sets with deterministic probability distributions. By utilizing a class of indicator functions and discrete-time Jensen inequality, delay-probability-distribution-dependent sufficient conditions are obtained in terms of linear matrix inequalities (LMIs) such that the discrete-time GRNs are robustly asymptotically stable in the mean-square sense for all admissible uncertainties and random delays. Three numerical examples are given to demonstrate the effectiveness of our theoretical results.

Robust H∞ control for uncertain discrete‐time systems with probabilistic state delays

AbstractIn this paper, we propose a novel design problem of robust H∞ control for discrete‐time systems with probabilistic time delay, where both the variation range of the delay and the probability distribution of the delay taking values in an interval are available. Based on the information on the probability distribution of the delay taking values in an interval, a new modeling method is put forward, with which the probabilistic effects of the delay are reflected into a parameter matrix of certain transformed system. Based on such a new model, criteria for the H∞ control design are derived by using a combination of the convexity of the matrix equations, the Lyapunov functional method and the linear matrix inequality technique. It is shown via numerical examples that our developed method in the paper can lead to less conservative results than those obtained by existing methods and, furthermore, if the probability distribution of the delay occurrence is available, the allowable upper bound of the delay may be larger than those derived for the case when only the variation range of the delay can be known. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

Macroscopic fluid flow conditions in spiral wound membrane elements: packed bed approach

The modelling of the reverse osmosis process is needed to fully evaluate its potential and facilitate scale up. The definition of the flow regime in the concentrate channel is of paramount importance. The present paper describes our experimental investigations on RTD and relates the RTD response curves to the regime of flow in the concentrate channel. Results demonstrate (i) that dead zones are present; (ii) that both a Plug Flow with Dispersion (PFD) and Probabilistic Time Delay (PTD) model can be used to characterise the flow; and (iii) that PFD- and PTD-model parameters assume nearly constant values for a given geometry which simplifies the prediction of the RTD for any desired flow rate.

Dynamics of probabilistic time delay models

Quantitative information on the dynamic behaviour of two general probabilistic time delay models, the gamma distributed model and the modified exponentially distributed model, is provided over wider ranges of model parameters than hitherto reported. The actual relationships that exist between the response and parameters of the gamma model, especially over an extended range of parameter values, are established relatively easily by recourse to frequency response. The results thus obtained are verified by a least squares curve fit of published experimental response data pertaining to a number of packed beds under trickle flow conditions. Certain characteristics that the modified exponential model has in common with the gamma model are identified. For both models, the existence of multiple sets of parameters for a given residence time distribution (RTD) curve (and consequent absence of unique parameter estimates) is also revealed.

A probabilistic time delay description of flow in packed beds

AbstractA simple model for describing residence time distributions (RTD) in packed beds is derived and applied to a trickle flow system. It is based on the concept of fluid elements being randomly delayed in time on their passage through the bed and leads to a simple and flexible mathematical description.