scholarly journals Computing the state difference equations for discrete overdetermined linear mD systems

Automatica ◽  
2016 ◽  
Vol 64 ◽  
pp. 254-261 ◽  
Author(s):  
Kim Batselier ◽  
Ngai Wong
Keyword(s):  
Difference Equations ◽  
The State ◽  
State Difference

scholarly journals Event-Triggering State and Fault Estimation for a Class of Nonlinear Systems Subject to Sensor Saturations

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1242
Author(s):  
Cong Huang ◽  
Bo Shen ◽  
Lei Zou ◽  
Yuxuan Shen
Keyword(s):  
Nonlinear Systems ◽  
Difference Equations ◽  
Estimation Error ◽  
Upper Bounds ◽  
The State ◽  
Fault Estimation ◽  
Triggering Mechanism ◽  
Transmission Frequency ◽  
Current Transmission ◽  
Event Triggering

This paper is concerned with the state and fault estimation issue for nonlinear systems with sensor saturations and fault signals. For the sake of avoiding the communication burden, an event-triggering protocol is utilized to govern the transmission frequency of the measurements from the sensor to its corresponding recursive estimator. Under the event-triggering mechanism (ETM), the current transmission is released only when the relative error of measurements is bigger than a prescribed threshold. The objective of this paper is to design an event-triggering recursive state and fault estimator such that the estimation error covariances for the state and fault are both guaranteed with upper bounds and subsequently derive the gain matrices minimizing such upper bounds, relying on the solutions to a set of difference equations. Finally, two experimental examples are given to validate the effectiveness of the designed algorithm.

scholarly journals Adaptive-illumination STED nanoscopy

2017 ◽  
Vol 114 (37) ◽  
pp. 9797-9802 ◽  
Author(s):  
Jörn Heine ◽  
Matthias Reuss ◽  
Benjamin Harke ◽  
Elisa D’Este ◽  
Steffen J. Sahl ◽  
...  
Keyword(s):  
Light Intensity ◽  
Biological Imaging ◽  
The State ◽  
Lower Intensity ◽  
2D And 3D ◽  
Imaging Conditions ◽  
State Difference

The concepts called STED/RESOLFT superresolve features by a light-driven transfer of closely packed molecules between two different states, typically a nonfluorescent “off” state and a fluorescent “on” state at well-defined coordinates on subdiffraction scales. For this, the applied light intensity must be sufficient to guarantee the state difference for molecules spaced at the resolution sought. Relatively high intensities have therefore been applied throughout the imaging to obtain the highest resolutions. At regions where features are far enough apart that molecules could be separated with lower intensity, the excess intensity just adds to photobleaching. Here, we introduce DyMIN (standing for Dynamic Intensity Minimum) scanning, generalizing and expanding on earlier concepts of RESCue and MINFIELD to reduce sample exposure. The principle of DyMIN is that it only uses as much on/off-switching light as needed to image at the desired resolution. Fluorescence can be recorded at those positions where fluorophores are found within a subresolution neighborhood. By tuning the intensity (and thus resolution) during the acquisition of each pixel/voxel, we match the size of this neighborhood to the structures being imaged. DyMIN is shown to lower the dose of STED light on the scanned region up to ∼20-fold under common biological imaging conditions, and >100-fold for sparser 2D and 3D samples. The bleaching reduction can be converted into accordingly brighter images at <30-nm resolution.

Factorial moments and probabilities for the general stochastic epidemic

1973 ◽  
Vol 10 (02) ◽  
pp. 277-288 ◽  
Author(s):  
L. Billard
Keyword(s):  
Difference Equations ◽  
The State ◽  
Factorial Moments ◽  
Stochastic Epidemic ◽  
The Matrix ◽  
Mean And Variance ◽  
The Mean ◽  
General Stochastic

By an appropriate partitioning of the matrix of coefficients in the system of differential difference equations for the general stochastic epidemic, the nature of the state probabilities is shown to consist of combinations of factorial terms. Further, factorial moments are readily obtained. In particular, the mean and variance of the number of susceptibles are derived.

Factorial moments and probabilities for the general stochastic epidemic

1973 ◽  
Vol 10 (2) ◽  
pp. 277-288 ◽  
Author(s):  
L. Billard
Keyword(s):  
Difference Equations ◽  
The State ◽  
Factorial Moments ◽  
Stochastic Epidemic ◽  
The Matrix ◽  
Mean And Variance ◽  
The Mean ◽  
General Stochastic

By an appropriate partitioning of the matrix of coefficients in the system of differential difference equations for the general stochastic epidemic, the nature of the state probabilities is shown to consist of combinations of factorial terms. Further, factorial moments are readily obtained. In particular, the mean and variance of the number of susceptibles are derived.

Coevolution of synchronization and cooperation in real networks

2019 ◽  
Vol 30 (07) ◽  
pp. 1940012 ◽  
Author(s):  
Mingyang Zhou ◽  
Xiaoyu Li ◽  
Wenman Xiong ◽  
Hao Liao
Keyword(s):  
Game Theory ◽  
Collective Behavior ◽  
Information Exchange ◽  
The State ◽  
Average Degree ◽  
Kuramoto Model ◽  
Necessary Condition ◽  
The Game Theory ◽  
The Cost ◽  
State Difference

As game theory thrives in networked interactions, we usually neglect the cost of information exchange between involved individuals. Individuals may decide (or refuse) to follow the state of their neighbors, which depends on the cost of the interactions. The payoff of a node’s behavior is associated with the state difference between the node and its neighbors. Here, based on Kuramoto model, we investigate the collective behavior of different individuals in the game theory and the synchronization byproduct that is induced by the cooperation of connected nodes. Specially, we investigate the influence of network structure on the coevolutionary progress of cooperation and synchronization. We find that the networks with the higher average degree are more likely to reach synchronization in real networks. Strong synchronization is a sufficient, but not necessary condition to guarantee the cooperation. Besides, we show that synchronization is largely influenced by the average degree in both Erdös–Rényi (ER) and Barabási–Albert (BA) networks, which is also illustrated by theoretical analysis.

Solution of jump parameter systems of differential and difference equations with semi-Markov coefficients

2003 ◽  
Vol 40 (2) ◽  
pp. 442-454 ◽  
Author(s):  
Efraim Shmerling ◽  
Kenneth J. Hochberg
Keyword(s):  
Asymptotic Stability ◽  
Markov Process ◽  
Difference Equations ◽  
The State ◽  
Systems Of Equations ◽  
Moment Equations ◽  
Semi Markov Process

We study linear jump parameter systems of differential and difference equations whose coefficients depend on the state of a semi-Markov process. We derive systems of equations for the first two moments of the random solutions of these jump parameter systems, and illustrate how moment equations can be used in examining their asymptotic stability.

Solution of jump parameter systems of differential and difference equations with semi-Markov coefficients

2003 ◽  
Vol 40 (02) ◽  
pp. 442-454 ◽  
Author(s):  
Efraim Shmerling ◽  
Kenneth J. Hochberg
Keyword(s):  
Asymptotic Stability ◽  
Markov Process ◽  
Difference Equations ◽  
The State ◽  
Systems Of Equations ◽  
Moment Equations ◽  
Semi Markov Process

We study linear jump parameter systems of differential and difference equations whose coefficients depend on the state of a semi-Markov process. We derive systems of equations for the first two moments of the random solutions of these jump parameter systems, and illustrate how moment equations can be used in examining their asymptotic stability.

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