Stochastic Time Delay Research Articles

Reaction-diffusion systems with stochastic time delay in kinetics

Time delay is an important dynamical issue in a multistep chemical reaction. We present a theoretical scheme for delayed reaction-diffusion systems where the time delay in kinetics is stochastic in nature. It has been shown that a small but finite strength of delay may result in generic change in the nature of spatiotemporal instability in the dynamics. Our theoretical analysis has been corroborated by numerical simulations on two reaction-diffusion systems.

Predictive control and scheduling codesign in network control systems

A codesign approach combining predictive control compensation and network scheduling is presented in this paper to overcome the adverse influences of stochastic time delays and packet losses encountered in network-based real-time control systems. The state estimation and control prediction compensation algorithms are used for the random network delays in the feedback and forward channels, and the stability criteria are analyzed. The proper sampling rate is given with network scheduling to meet the desired system performance, while the network-induced delay is tolerated. Simulations show that the codesign approach works well with the bounded network delay.

Predictive control for vehicular sensor networks based on round-trip time-delay prediction

With the rapid development of vehicular sensor networks (VSNs) technology, the potential use of networked real-time control and automation is enormous and appealing. However, closed-loop control VSNs via the Internet are very difficult to implement practically because of their stochastic nature. One of the biggest challenges in VSNs is how to deal with sensor networks time delay and data loss. The authors investigate the potential of using the predictive control scheme for VSNs based on round-trip time (RTT) delay prediction to overcome the VSNs transmission delay and data loss. The predicted RTT delay is taken as the sampling interval reference for variable-period sampling approach. Modelling the time delay of networked control systems as a non-linear time series, the least mean square (LMS) filter algorithm is adopted to predict online the time delay induced in VSNs. The simulation results show that the LMS algorithm can achieve ideal efficacy if time delay has no variety abnormally. The predictive compensation strategy is proposed to reduce the detrimental effect of stochastic time delays induced by communication networks on control performance. The results of offline simulations via the Internet illustrate that the predictive control scheme based on RTT delay prediction has the potential to overcome the VSNs time delay and data loss.

WE-D-211A-02: Modeling and Error Analysis of the Clinical Process in Radiation Therapy

Purpose: To evaluate use of Petri nets industrial system modeling tool for error pathway analysis and error prevention in radiation therapy (RT). Materials and Methods: Petri nets are a common and easily accessible tool for modeling state and event based systems. A Petri net includes “state‐like” objects and “event‐like” objects and the dependencies between the objects. The complete system is represented as a graph consisting of places (states) and transitions (state changes due to occurring events) that are connected by directed arcs. The places on the net can contain any number of mobile elements of the system, referred to as tokens. These tokens are moved from place to place by the “firing” of the transition representing an event in the system. A transition does not have to fire immediately when a token is added to an input place. It may instead have a deterministic or stochastic time delay. Petri nets with randomness in the transitions are called Stochastic Petri Nets. This representation would allow thorough analysis of the system activities. We designed a Petri net representation of our clinical workflow and represented events as transitions and cause for the events as the states. We have collected more than 1000 events through our electronic error reporting software and used Petri Nets to analyze the data. Results: We could identify the fault events and their propagation through the system. We could estimate the corresponding failure probabilities at different stages and their impact on the treatment process. In addition, we can investigate the effects of workflow alteration and patient load on the system performance, and identify optimal system design schemes. Conclusions: The proposed Petri Net approach can achieve early failure detection as well as facilitate event quantification. This can be used for the improvement of patient care and processes in RT.

Robust filtering for stochastic genetic regulatory networks with time-varying delay

This paper addresses the robust filtering problem for a class of linear genetic regulatory networks (GRNs) with stochastic disturbances, parameter uncertainties and time delays. The parameter uncertainties are assumed to reside in a polytopic region, the stochastic disturbance is state-dependent described by a scalar Brownian motion, and the time-varying delays enter into both the translation process and the feedback regulation process. We aim to estimate the true concentrations of mRNA and protein by designing a linear filter such that, for all admissible time delays, stochastic disturbances as well as polytopic uncertainties, the augmented state estimation dynamics is exponentially mean square stable with an expected decay rate. A delay-dependent linear matrix inequality (LMI) approach is first developed to derive sufficient conditions that guarantee the exponential stability of the augmented dynamics, and then the filter gains are parameterized in terms of the solution to a set of LMIs. Note that LMIs can be easily solved by using standard software packages. A simulation example is exploited in order to illustrate the effectiveness of the proposed design procedures.

Filtering for Nonlinear Genetic Regulatory Networks With Stochastic Disturbances

In this paper, the filtering problem is investigated for nonlinear genetic regulatory networks with stochastic disturbances and time delays, where the nonlinear function describing the feedback regulation is assumed to satisfy the sector condition, the stochastic perturbation is in the form of a scalar Brownian motion, and the time delays exist in both the translation process and the feedback regulation process. The purpose of the addressed filtering problem is to estimate the true concentrations of the mRNA and protein. Specifically, we are interested in designing a linear filter such that, in the presence of time delays, stochastic disturbances as well as sector nonlinearities, the filtering dynamics of state estimation for the stochastic genetic regulatory network is exponentially mean square stable with a prescribed decay rate lower bound beta. By using the linear matrix inequality (LMI) technique, sufficient conditions are first derived for ensuring the desired filtering performance for the gene regulatory model, and the filter gain is then characterized in terms of the solution to an LMI, which can be easily solved by using standard software packages. A simulation example is exploited in order to illustrate the effectiveness of the proposed design procedures.

Stabilization of Networked Control System with Time Delays and Data-packet Losses

In this paper, we provide experimental results in the application of the results of [4]. Based on the theoretic work in [4], we propose an estimator-based delaycompensation algorithm to stabilize a networked control system (NCS) with network-induced stochastic time delays, data-packet losses, and out-of-order data-packet transmissions. With the p-sampling-period delay upper bound, the NCS can also accommodate up to p – 1 successive packet losses. We also derive sufficient conditions for the stability of the NCS. The feasibility and effectiveness of the theoretic results of [4] is verified experimentally using an NCS test bed incorporating an open-loop unstable ball magnetic-levitation (maglev) system we constructed.

Networked Real-Time Control Strategy Dealing With Stochastic Time Delays and Packet Losses

Abstract A novel model-predictive-control strategy with a timeout scheme and p-step-ahead state estimation is presented in this paper to overcome the adverse influences of stochastic time delays and packet losses encountered in network-based distributed real-time control. An open-loop unstable magnetic-levitation (maglev) test bed was constructed and employed for its experimental verification. The compensation algorithms developed in this paper deal with the network-induced stochastic time delays and packet losses in both the forward path and the feedback path simultaneously. With the p-sampling-period delay upper bound, the networked control system (NCS) can also accommodate up to p−1 successive packet losses. Experimental results demonstrate the feasibility and effectiveness of this networked real-time control strategy.

Applying a Generalized Predictive Control Theory to a Carding Autoleveler

Usually, a carding process is difficult to control with classic control algorithms (such as PID) for three main reasons: strong stochastic disturbance, time delays, and parameter variation. In this paper, generalized predictive control (GPC) is introduced to control such a process. First, a CARIMA model is built to describe the carding process, then the GPC control law is derived and used to design the controller for a carding autoleveler. The simulation results show that the GPC controller can greatly reduce a sliver's standard deviation and can reject measured and unmeasured step disturbance. Although this paper mainly involves the design of a feedforward-feedback GPC controller for a carding autoleveler, the methods of modeling and GPC controller design can easily be extended to a feedback case and used to design controllers for other preparatory machines' autolev elers.

Control of a Robot Car Through WEB

In this work the control of a robot car, i.e. automated guided vehicle, using Internet has been investigated. The case of the open-loop control system for such a robot car under remote command supervision via Internet has been explored and resolved only. Complete systems engineering design involving electronics hardware on the model robot and two-way radio communication subsystem as well as the real-time and applications software subsystems hasbeen carried out, and fully implemented. Extensive experimental testing via remotestation at several places in Turkey have been performed. The results obtained were satisfactory always. The workcontinues further on the case of the closed-loop system of robot car via Internet. In the case of closed-loop system design concept, due to stochastic time delays, some additional problems are expected and have to be investigated.

The effect of stochastic time delays on the reliability of isolated impulse systems

AbstractThis article concerns the effect of stochastic time delays in the operation of components upon system reliability for isolated impulse systems, for which component delays have hitherto been treated as deterministic. These are systems, such as automatic protective devices, which remain idle for most of their lives but which are required to respond with the utmost speed to input signals arising at arbitrary isolated time instants. System failure can arise from components failing to operate, or from being too slow to operate so that the systems operation is too slow to meet requirements. During operation components are usually subjected to greater stresses than during idling, so that it is assumed that components are subjected to increased failure tendencies during the time it takes them to perform their functions. The effect of stochastic time delays on the evaluation of systems reliability is considered, and a hierarchy of complexity associated with the physical nature of the delays in series and redundant configurations is exposed. Some simple exponential illustrations are presented.

BValues for foreshocks and aftershocks in real and simulated earthquake sequences

abstractThe differences in b values between foreshock and aftershock sequences can be shown to be a statistically significant property of real earthquake sequences if a sufficiently large number of cases is considered, i.e., if the catalogs are long enough. These differences depend on the particulars of the data processing procedures used to define the sequences, such as space-time windowing and definition of cutoff magnitude thresholds for completeness of catalogs, as well as other magnitude cutoffs. They are also a statistically significant property of long artificial, or synthetic catalogs in which all subsequent earthquakes are modeled as resulting from a stochastic time delay applied to predecessor earthquakes. As a consequence, we make the conjecture that the difference in b values is due to subtle asymmetries in data processing procedures rather than differences in the physical environment before and after a large earthquake.

Linear Population Models with Stochastic Time Delays

Previously it was shown that reproductive—cycle parameters such as time to maturity, ovulation interval, gestation period, duration of regression, duration of nonreproductive lactation period, and the like, can be incorporated into population models rather easily through the use of a simple network approach. In this paper, the network approach is extended to include the same types of reproductive parameters when their values are not necessarily fixed, but may vary randomly from one member of a population to the next and/or for a given member from one time to the next. It is shown that linear transforms of the parameter distribution functions can be incorporated directly into the network models and that analysis of the resulting dynamics follows in a straightforward manner, the characteristic dynamical equation being obtainable by inspection with Mason's algorithm and the roots of the equation being obtainable by direct analysis in simple cases or by well—established numerical methods in complicated cases. The roots themselves can be interpreted directly in terms of dominant patterns of population growth and deduced propensity of the population to sustain oscillations triggered by external stimuli. In the case of a simple natality cycle with gamma, negative binomial, and binomial distributions of maturation times, it is shown that the dominant growth pattern approximates rather closely that expected for a nonrandom maturation time equal to the mean of the distribution, and that the propensity to sustain population oscillations decreases markedly both with increasing standard deviation and with increasing (positive) skewness in the distribution.

Queuing Analysis of Satellite Networks

This paper models satellite communications systems by means of bipartite graphs. It assumes stochastic inputs and time delay is the factor of interest. The paper formulates the model and describes the routing and digital transmission schemes, assuming the network links to be synchronized. Messages may be transmitted only in the synchronized time slots, on a first-come first-served basis. The queuing problem is discussed for the single branch and for the satellite network cases, and approximate solutions are obtained for the case of satellites with finite memories.