Act-and-wait control of discrete systems with random delays

Ghasemi, Mohammadreza; Zhao, Siming; Insperger, Tamás; Kalmár‐Nagy, Tamás

doi:10.1109/acc.2012.6315674

Cited by 8 publications

(6 citation statements)

References 22 publications

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“…Using multivariate Taylor's expansion (around x 0 ϭ 0) we obtain the following power series representations (8) where and denotes the Kroncker's product. Therefore, the system (7) can be written in the form (9) where the dots represent higher order terms. To determine the first N kernels corresponding to the system (9), differential equations are developed for x (i) , 2 Յ i Յ N. The differential equation of x (i) takes the form (10) The coefficients a i, k are given by a 1, k (t) ϭ a k (t), and for i Ͼ 1 (11) where the number of terms is i and there are i -1 Kronecker products.…”

Section: Carleman Bilinearizationmentioning

confidence: 99%

“…This problem is revealed more in natural and hydraulic fracture and unconventional reservoir models [18], as well as intensive frameworks, such as history matching, production optimization, uncertainty quantification [12,11]. Also, the computational time of such large-scale models become the bottleneck of fast turnarounds in the decision-making process and assimilating realtime data into the model [5,9].…”

Section: Introductionmentioning

confidence: 99%

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Reduced Order Modeling In Reservoir Simulation Using the Bilinear Approximation Techniques

Ghasemi

Ibrahim

Gildin

2014

SPE Latin America and Caribbean Petroleum Engineering Conference

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Despite great advances in reservoir simulation capabilities with the introduction of high-performance computing (HPC) platforms and enhanced solvers, high fidelity grid-based simulation still remains a challenging task. This task is especially demanding for fine-resolved geological reservoirs with multiphase and multicomponents and in production optimization and uncertainty quantification frameworks where several calls of the large scale simulation model need to be performed. Model order reduction techniques have been applied in porous media flow modeling in order to obtain fast simulation surrogates to alleviate the high computational cost associated with these simulations. The difficulty of applying model reduction techniques to porous media flow arises from the nonlinearity of the system. In order to overcome the issue of nonlinearity, we introduce the bilinear form of the dynamical system which in many cases produces a satisfying approximation of the system. The bilinear approximation is a simple form of the parent system and it is linear in the input and linear in the state but it not linear in both jointly. The bilinear form is computed using truncated multidimensional Taylor's expansion of the system terms. Examples are presented to illustrate this recent approach for the case of single phase flow modeling, and comparisons are made with the case of linearized models and the full nonlinear models. In addition, we present methods to reduce the complexity of the bilinear system of equations and results are presented that compare linear model reduction (balanced truncation) and nonlinear model reductions, such as POD techniques.

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Section: Carleman Bilinearizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Reduced Order Modeling In Reservoir Simulation Using the Bilinear Approximation Techniques

Ghasemi

Ibrahim

Gildin

2014

SPE Latin America and Caribbean Petroleum Engineering Conference

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“…Consequently, an accurate analysis of uncertainty requires a large number of simulations (Camacho et al, 2017;Lee et al, 2014;Yang et al, 2007;Yeh et al, 2014). Furthermore, the computational time of large-scale refined models becomes a bottleneck in the decision-making process and assimilating real-time data into a model (Ghasemi et al, 2012;Gildin and Lopez, 2011;Salehi, 2016;Salehi et al, 2013). In all of the reservoir studies areas mentioned above, there have always been attempts to accelerate simulations in order to overcome their prohibitive costs and make them feasible for real-world applications while honoring the accuracy and reliability of the outcome.…”

Section: Introductionmentioning

confidence: 99%

A General Spatio-Temporal Clustering-Based Non-Local Formulation for Multiscale Modeling of Compartmentalized Reservoirs

Esmaeilzadeh

Salehi

Hetz

et al. 2019

SPE Western Regional Meeting

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Quantum Reservoir Impact LLC, TX, USA AbstractRepresenting the reservoir as a network of discrete compartments with neighbor and non-neighbor connections is a fast, yet accurate method for analyzing oil and gas reservoirs. Automatic and rapid detection of coarse-scale compartments with distinct static and dynamic properties is an integral part of such high-level reservoir analysis. In this work, we present a hybrid framework specific to reservoir analysis for an automatic detection of clusters in space using spatial and temporal field data, coupled with a physics-based multiscale modeling approach. A novel and rigorous non-local formulation for flow in porous media is presented, in which the reservoir is represented by an adjacency matrix describing the connectivities of comprising compartments. We automatically divide the reservoir into a number of distinct compartments, in which the directiondependent multiphase flow communication is a function of non-local phase potential differences. Our proposed clustering framework begins with a mixed-type raw dataset which can be categorical/numerical, spatial/temporal, and discrete/continuous. The dataset can contain noisy/missing values of different data types including but not limited to well production/injection history, well location, well type, geological features, PVT measurements, perforation data, etc. Unsupervised clustering techniques suited to the input data types (e.g. k-prototypes, spectral, Gaussian Mixtures, and hierarchical clustering), and appropriate distance measures (such as Euclidean distance, soft dynamic time warping, and mode) are used. The input data is standardized, and upon convergence check, the best clustering representation is obtained. Finally, Support-Vector-Machine technique is utilized in the kernel space to trace a demarcating hyperplane for the clusters. The proposed framework is successfully applied to more than five mature fields in the Middle East, South and North America, each with more than a thousand wells. In a specific case study reported here, the proposed workflow is applied to a major field with a couple of hundreds of wells with more than 40 years of production history. Leveraging the fast forward model, an efficient ensemble-based history matching framework is applied to reduce the uncertainty of the global reservoir parameters such as inter-blocks and aquifer-reservoir communications, fault transmissibilities, and block-based oil in place. The ensemble of history matched models are then used to provide a probabilistic forecast for different field development scenarios. In addition, the clustering framework enables us to treat missing data and use the augmented dataset for improving the clustering accuracy. In summary, in this work a novel hybrid approach is presented in which we couple a physics-based non-local modeling framework with data-driven clustering techniques to provide a fast and accurate multiscale modeling of compartmentalized reservoirs. This research also adds to the literature by presenting a comprehensive w...

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“…Similarly, taking the worst case scenario (e.g., largest delay) can lead to unnecessary conservativeness or may simply give erroneous results. Even ensuring stability for each value of the delay does not necessarily give the stability of the stochastic system [13]. …”

Section: Introductionmentioning

confidence: 99%

Stability of Systems with Stochastic Delays and Applications to Genetic Regulatory Networks

Gomez¹,

Sadeghpour²,

Bennett³

et al. 2016

SIAM J. Appl. Dyn. Syst.

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The dynamics of systems with stochastically varying time delays are investigated in this paper. It is shown that the mean dynamics can be used to derive necessary conditions for the stability of equilibria of the stochastic system. Moreover, the second moment dynamics can be used to derive sufficient conditions for almost sure stability of equilibria. The results are summarized using stability charts that are obtained via semi-discretization. The theoretical methods are applied to simple gene regulatory networks where it is demonstrated that stochasticity in the delay can improve the stability of steady protein production.

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Act-and-wait control of discrete systems with random delays

Cited by 8 publications

References 22 publications

Reduced Order Modeling In Reservoir Simulation Using the Bilinear Approximation Techniques

Reduced Order Modeling In Reservoir Simulation Using the Bilinear Approximation Techniques

A General Spatio-Temporal Clustering-Based Non-Local Formulation for Multiscale Modeling of Compartmentalized Reservoirs

Stability of Systems with Stochastic Delays and Applications to Genetic Regulatory Networks

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