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Arjan Van Der Schaft - One of the best experts on this subject based on the ideXlab platform.
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Physical Network Systems and Model Reduction
Mathematical Control Theory II, 2015Co-Authors: Arjan Van Der SchaftAbstract:The common structure of a number of Physical Network systems is identified, based on the incidence structure of the graph, the weights associated to the edges, and the total stored energy. State variables may not only be associated to the vertices, but also to the edges of the graph; in clear contrast with multiagent systems. Structure-preserving model reduction concerns the problem of approximating a complex Physical Network system by a system of lesser complexity, but within the same class of Physical Network systems. Two approaches, respectively, based on clustering and on Kron reduction, are explored.
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Structure-preserving model reduction of Physical Network systems by clustering
arXiv: Systems and Control, 2014Co-Authors: Nima Monshizadeh, Arjan Van Der SchaftAbstract:In this paper, we establish a method for model order reduction of a certain class of Physical Network systems. The proposed method is based on clustering of the vertices of the underlying graph, and yields a reduced order model within the same class. To capture the Physical properties of the Network, we allow for weights associated to both the edges as well as the vertices of the graph. We extend the notion of almost equitable partitions to this class of graphs. Consequently, an explicit model reduction error expression in the sense of H2-norm is provided for clustering arising from almost equitable partitions. Finally the method is extended to second-order systems.
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CDC - Structure-preserving model reduction of Physical Network systems by clustering
53rd IEEE Conference on Decision and Control, 2014Co-Authors: Nima Monshizadeh, Arjan Van Der SchaftAbstract:In this paper, we establish a method for model order reduction of a certain class of Physical Network systems. The proposed method is based on clustering of the vertices of the underlying graph, and yields a reduced order model within the same class. To capture the Physical properties of the Network, we allow for weights associated to both the edges as well as the vertices of the graph. We extend the notion of almost equitable partitions to this class of graphs. Consequently, an explicit model reduction error expression in the sense of ℋ 2 -norm is provided for clustering arising from almost equitable partitions. Finally the method is extended to second-order systems.
Petar Popovski - One of the best experts on this subject based on the ideXlab platform.
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optimized constellations for two way wireless relaying with Physical Network coding
IEEE Journal on Selected Areas in Communications, 2009Co-Authors: Toshiaki Koikeakino, Petar Popovski, Vahid TarokhAbstract:We investigate modulation schemes optimized for two-way wireless relaying systems, for which Network coding is employed at the Physical layer. We consider Network coding based on denoise-and-forward (DNF) protocol, which consists of two stages: multiple access (MA) stage, where two terminals transmit simultaneously towards a relay, and broadcast (BC) stage, where the relay transmits towards the both terminals. We introduce a design principle of modulation and Network coding, considering the superposed constellations during the MA stage. For the case of QPSK modulations at the MA stage, we show that QPSK constellations with an exclusive-or (XOR) Network coding do not always offer the best transmission for the BC stage, and that there are several channel conditions in which unconventional 5-ary constellations lead to a better throughput performance. Through the use of sphere packing, we optimize the constellation for such an irregular Network coding. We further discuss the design issue of the modulation in the case when the relay exploits diversity receptions such as multiple-antenna diversity and path diversity in frequency-selective fading. In addition, we apply our design strategy to a relaying system using higher-level modulations of 16QAM in the MA stage. Performance evaluations confirm that the proposed scheme can significantly improve end-to-end throughput for two-way relaying systems.
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Physical Network coding in two way wireless relay channels
arXiv: Information Theory, 2007Co-Authors: Petar Popovski, Hiroyuki YomoAbstract:It has recently been recognized that the wireless Networks represent a fertile ground for devising communication modes based on Network coding. A particularly suitable application of the Network coding arises for the two--way relay channels, where two nodes communicate with each other assisted by using a third, relay node. Such a scenario enables application of \emph{Physical Network coding}, where the Network coding is either done (a) jointly with the channel coding or (b) through Physical combining of the communication flows over the multiple access channel. In this paper we first group the existing schemes for Physical Network coding into two generic schemes, termed 3--step and 2--step scheme, respectively. We investigate the conditions for maximization of the two--way rate for each individual scheme: (1) the Decode--and--Forward (DF) 3--step schemes (2) three different schemes with two steps: Amplify--and--Forward (AF), JDF and Denoise--and--Forward (DNF). While the DNF scheme has a potential to offer the best two--way rate, the most interesting result of the paper is that, for some SNR configurations of the source--relay links, JDF yields identical maximal two--way rate as the upper bound on the rate for DNF.
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Physical Network coding in two way wireless relay channels
International Conference on Communications, 2007Co-Authors: Petar Popovski, Hiroyuki YomoAbstract:It has recently been recognized that the wireless Networks represent a fertile ground for devising communication modes based on Network coding. A particularly suitable application of the Network coding arises for the two-way relay channels, where two nodes communicate with each other assisted by using a third, relay node. Such a scenario enables application of Physical Network coding, where the Network coding is either done (a) jointly with the channel coding or (b) through Physical combining of the communication flows over the multiple access channel. In this paper we first group the existing schemes for Physical Network coding into two generic schemes, termed 3-step and 2-step scheme, respectively. We investigate the conditions for maximization of the two-way rate for each individual scheme: (1) the decode-and-forward (DF) 3-step schemes (2) three different schemes with two steps: amplify-and-forward (AF), JDF and denoise-and-forward (DNF). While the DNF scheme has a potential to offer the best two-way rate, the most interesting result of the paper is that, for some SNR configurations of the source - relay links, JDF yields identical maximal two-way rate as the upper bound on the rate for DNF.
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ICC - Physical Network Coding in Two-Way Wireless Relay Channels
2007 IEEE International Conference on Communications, 2007Co-Authors: Petar Popovski, Hiroyuki YomoAbstract:It has recently been recognized that the wireless Networks represent a fertile ground for devising communication modes based on Network coding. A particularly suitable application of the Network coding arises for the two-way relay channels, where two nodes communicate with each other assisted by using a third, relay node. Such a scenario enables application of Physical Network coding, where the Network coding is either done (a) jointly with the channel coding or (b) through Physical combining of the communication flows over the multiple access channel. In this paper we first group the existing schemes for Physical Network coding into two generic schemes, termed 3-step and 2-step scheme, respectively. We investigate the conditions for maximization of the two-way rate for each individual scheme: (1) the decode-and-forward (DF) 3-step schemes (2) three different schemes with two steps: amplify-and-forward (AF), JDF and denoise-and-forward (DNF). While the DNF scheme has a potential to offer the best two-way rate, the most interesting result of the paper is that, for some SNR configurations of the source - relay links, JDF yields identical maximal two-way rate as the upper bound on the rate for DNF.
Anatoly Zlotnik - One of the best experts on this subject based on the ideXlab platform.
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Monotonicity Properties of Physical Network Flows and Application to Robust Optimal Allocation
arXiv: Optimization and Control, 2020Co-Authors: Sidhant Misra, Marc Vuffray, Anatoly ZlotnikAbstract:We derive conditions for monotonicity properties that characterize general flows of a commodity over a Network, where the flow is described by potential and flow dynamics on the edges, as well as potential continuity and Kirchhoff-Neumann mass balance requirements at nodes. The transported commodity may be injected or withdrawn at any of the Network nodes, and its movement throughout the Network is controlled by nodal actuators. For a class of dissipative nonlinear parabolic partial differential equation (PDE) systems on Networks, we derive conditions for monotonicity properties in steady-state flow, as well as for propagation of monotone ordering of states with respect to time-varying boundary condition parameters. In the latter case, initial conditions, as well as time-varying parameters in the coupling conditions at vertices, provide an initial boundary value problem (IBVP). We prove that ordering properties of the solution to the IBVP are preserved when the initial conditions and the parameters of the time-varying coupling law are appropriately ordered. Then, we prove that when monotone ordering is not preserved, the first crossing of solutions occurs at a Network node. We consider the implications for robust optimization and optimal control formulations and real-time monitoring of uncertain dynamic flows on Networks, and discuss application to subsonic compressible fluid flow with energy dissipation on Physical Networks. The main result and monitoring policy are demonstrated for gas pipeline test Networks and a case study using data corresponding to a real working system. We propose applications of this general result to the control and monitoring of natural gas transmission Networks.
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Monotonicity Properties of Physical Network Flows and Application to Robust Optimal Allocation
Proceedings of the IEEE, 2020Co-Authors: Sidhant Misra, Marc Vuffray, Anatoly ZlotnikAbstract:We derive conditions for monotonicity properties that characterize general flows of a commodity over a Network, where the flow is described by potential and flow dynamics on the edges, as well as potential continuity and the Kirchhoff–Neumann mass balance requirements at nodes. The transported commodity may be injected or withdrawn at any of the Network nodes, and its movement throughout the Network is controlled by nodal actuators. For a class of dissipative nonlinear parabolic partial differential equation (PDE) systems on Networks, we derive conditions for monotonicity properties in steady-state flow, as well as for propagation of monotone ordering of states with respect to time-varying boundary condition parameters. In the latter case, initial conditions and time-varying parameters in the coupling conditions at vertices provide an initial boundary value problem (IBVP). We prove that ordering properties of the solution to the IBVP are preserved when the initial conditions and the parameters of the time-varying coupling law are appropriately ordered. Then, we prove that when monotone ordering is not preserved, the first crossing of solutions occurs at a Network node. We consider the implications for robust optimization and optimal control formulations and real-time monitoring of uncertain dynamic flows on Networks and discuss the application to subsonic compressible fluid flow with energy dissipation on Physical Networks. The main result and monitoring policy are demonstrated for gas pipeline test Networks and a case study using data corresponding to a real working system. We propose applications of this general result to the control and monitoring of natural gas transmission Networks.
Hiroyuki Yomo - One of the best experts on this subject based on the ideXlab platform.
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Physical Network coding in two way wireless relay channels
arXiv: Information Theory, 2007Co-Authors: Petar Popovski, Hiroyuki YomoAbstract:It has recently been recognized that the wireless Networks represent a fertile ground for devising communication modes based on Network coding. A particularly suitable application of the Network coding arises for the two--way relay channels, where two nodes communicate with each other assisted by using a third, relay node. Such a scenario enables application of \emph{Physical Network coding}, where the Network coding is either done (a) jointly with the channel coding or (b) through Physical combining of the communication flows over the multiple access channel. In this paper we first group the existing schemes for Physical Network coding into two generic schemes, termed 3--step and 2--step scheme, respectively. We investigate the conditions for maximization of the two--way rate for each individual scheme: (1) the Decode--and--Forward (DF) 3--step schemes (2) three different schemes with two steps: Amplify--and--Forward (AF), JDF and Denoise--and--Forward (DNF). While the DNF scheme has a potential to offer the best two--way rate, the most interesting result of the paper is that, for some SNR configurations of the source--relay links, JDF yields identical maximal two--way rate as the upper bound on the rate for DNF.
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Physical Network coding in two way wireless relay channels
International Conference on Communications, 2007Co-Authors: Petar Popovski, Hiroyuki YomoAbstract:It has recently been recognized that the wireless Networks represent a fertile ground for devising communication modes based on Network coding. A particularly suitable application of the Network coding arises for the two-way relay channels, where two nodes communicate with each other assisted by using a third, relay node. Such a scenario enables application of Physical Network coding, where the Network coding is either done (a) jointly with the channel coding or (b) through Physical combining of the communication flows over the multiple access channel. In this paper we first group the existing schemes for Physical Network coding into two generic schemes, termed 3-step and 2-step scheme, respectively. We investigate the conditions for maximization of the two-way rate for each individual scheme: (1) the decode-and-forward (DF) 3-step schemes (2) three different schemes with two steps: amplify-and-forward (AF), JDF and denoise-and-forward (DNF). While the DNF scheme has a potential to offer the best two-way rate, the most interesting result of the paper is that, for some SNR configurations of the source - relay links, JDF yields identical maximal two-way rate as the upper bound on the rate for DNF.
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ICC - Physical Network Coding in Two-Way Wireless Relay Channels
2007 IEEE International Conference on Communications, 2007Co-Authors: Petar Popovski, Hiroyuki YomoAbstract:It has recently been recognized that the wireless Networks represent a fertile ground for devising communication modes based on Network coding. A particularly suitable application of the Network coding arises for the two-way relay channels, where two nodes communicate with each other assisted by using a third, relay node. Such a scenario enables application of Physical Network coding, where the Network coding is either done (a) jointly with the channel coding or (b) through Physical combining of the communication flows over the multiple access channel. In this paper we first group the existing schemes for Physical Network coding into two generic schemes, termed 3-step and 2-step scheme, respectively. We investigate the conditions for maximization of the two-way rate for each individual scheme: (1) the decode-and-forward (DF) 3-step schemes (2) three different schemes with two steps: amplify-and-forward (AF), JDF and denoise-and-forward (DNF). While the DNF scheme has a potential to offer the best two-way rate, the most interesting result of the paper is that, for some SNR configurations of the source - relay links, JDF yields identical maximal two-way rate as the upper bound on the rate for DNF.
Nima Monshizadeh - One of the best experts on this subject based on the ideXlab platform.
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Structure-preserving model reduction of Physical Network systems by clustering
arXiv: Systems and Control, 2014Co-Authors: Nima Monshizadeh, Arjan Van Der SchaftAbstract:In this paper, we establish a method for model order reduction of a certain class of Physical Network systems. The proposed method is based on clustering of the vertices of the underlying graph, and yields a reduced order model within the same class. To capture the Physical properties of the Network, we allow for weights associated to both the edges as well as the vertices of the graph. We extend the notion of almost equitable partitions to this class of graphs. Consequently, an explicit model reduction error expression in the sense of H2-norm is provided for clustering arising from almost equitable partitions. Finally the method is extended to second-order systems.
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CDC - Structure-preserving model reduction of Physical Network systems by clustering
53rd IEEE Conference on Decision and Control, 2014Co-Authors: Nima Monshizadeh, Arjan Van Der SchaftAbstract:In this paper, we establish a method for model order reduction of a certain class of Physical Network systems. The proposed method is based on clustering of the vertices of the underlying graph, and yields a reduced order model within the same class. To capture the Physical properties of the Network, we allow for weights associated to both the edges as well as the vertices of the graph. We extend the notion of almost equitable partitions to this class of graphs. Consequently, an explicit model reduction error expression in the sense of ℋ 2 -norm is provided for clustering arising from almost equitable partitions. Finally the method is extended to second-order systems.
