Pub Date : 2015-09-01DOI: 10.1109/ALLERTON.2015.7447044
F. Rego, Ye Pu, A. Alessandretti, Antonio Pedro Aguiar, C. Jones
In this paper we address the problem of quantized consensus where process noise or external inputs corrupt the state of each agent at each iteration. We propose a quantized consensus algorithm with progressive quantization, where the quantization interval changes in length at each iteration by a pre-specified value. We derive conditions on the design parameters of the algorithm to guarantee ultimate boundedness of the deviation from the average of each agent. Moreover, we determine explicitly the bounds of the consensus error under the assumption that the process disturbances are ultimately bounded within known bounds. A numerical example of cooperative path-following of a network of single integrators illustrates the performance of the proposed algorithm.
{"title":"A consensus algorithm for networks with process noise and quantization error","authors":"F. Rego, Ye Pu, A. Alessandretti, Antonio Pedro Aguiar, C. Jones","doi":"10.1109/ALLERTON.2015.7447044","DOIUrl":"https://doi.org/10.1109/ALLERTON.2015.7447044","url":null,"abstract":"In this paper we address the problem of quantized consensus where process noise or external inputs corrupt the state of each agent at each iteration. We propose a quantized consensus algorithm with progressive quantization, where the quantization interval changes in length at each iteration by a pre-specified value. We derive conditions on the design parameters of the algorithm to guarantee ultimate boundedness of the deviation from the average of each agent. Moreover, we determine explicitly the bounds of the consensus error under the assumption that the process disturbances are ultimately bounded within known bounds. A numerical example of cooperative path-following of a network of single integrators illustrates the performance of the proposed algorithm.","PeriodicalId":112948,"journal":{"name":"2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125631918","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-09-01DOI: 10.1109/ALLERTON.2015.7447015
Subrahmanya Swamy Peruru, R. Ganti, K. Jagannathan
In this paper, we consider an adaptive CSMA based scheduling algorithm for a single-hop wireless network under a realistic SINR (signal-to-interference-plus-noise ratio) model for the interference, and propose an efficient local optimization based algorithm to estimate certain parameters of the algorithm called fugacities. It is known that adaptive CSMA based algorithms can achieve throughput optimality, by sampling feasible schedules from a Gibbs distribution with appropriate fugacities. Unfortunately, estimating the optimal fugacities for a desired service rate vector is an NP-hard problem. Further, the existing adaptive CSMA algorithms use a stochastic gradient descent based method, which usually entails an impractically slow (exponential in the size of the network) convergence to the optimal fugacities. In contrast, the convergence rate and the complexity of our algorithm is independent of the network size, and depends only on the neighborhood size of a link. In particular, in spatial networks where the neighborhood size does not scale with the network size, our algorithm is order optimal. We show that the proposed algorithm corresponds exactly to performing the well-known Bethe approximation to the underlying Gibbs distribution. We also consider two special cases of the SINR interference model and obtain the corresponding fugacities in closed form. Numerical results indicate that the proposed method achieves extremely fast convergence to near-optimal fugacities, and often outperforms the convergence rate of the stochastic gradient descent by a few orders of magnitude.
{"title":"Adaptive CSMA under the SINR model: Fast convergence through local gibbs optimization","authors":"Subrahmanya Swamy Peruru, R. Ganti, K. Jagannathan","doi":"10.1109/ALLERTON.2015.7447015","DOIUrl":"https://doi.org/10.1109/ALLERTON.2015.7447015","url":null,"abstract":"In this paper, we consider an adaptive CSMA based scheduling algorithm for a single-hop wireless network under a realistic SINR (signal-to-interference-plus-noise ratio) model for the interference, and propose an efficient local optimization based algorithm to estimate certain parameters of the algorithm called fugacities. It is known that adaptive CSMA based algorithms can achieve throughput optimality, by sampling feasible schedules from a Gibbs distribution with appropriate fugacities. Unfortunately, estimating the optimal fugacities for a desired service rate vector is an NP-hard problem. Further, the existing adaptive CSMA algorithms use a stochastic gradient descent based method, which usually entails an impractically slow (exponential in the size of the network) convergence to the optimal fugacities. In contrast, the convergence rate and the complexity of our algorithm is independent of the network size, and depends only on the neighborhood size of a link. In particular, in spatial networks where the neighborhood size does not scale with the network size, our algorithm is order optimal. We show that the proposed algorithm corresponds exactly to performing the well-known Bethe approximation to the underlying Gibbs distribution. We also consider two special cases of the SINR interference model and obtain the corresponding fugacities in closed form. Numerical results indicate that the proposed method achieves extremely fast convergence to near-optimal fugacities, and often outperforms the convergence rate of the stochastic gradient descent by a few orders of magnitude.","PeriodicalId":112948,"journal":{"name":"2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"351 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134408900","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-09-01DOI: 10.1109/ALLERTON.2015.7447126
P. Wang, R. Safavi-Naini, Fuchun Lin
In an erasure adversarial wiretap channel (eAWTP-channel), the adversary can select a fraction ρr of the codeword to read, and a fraction ρe of the codeword to erase. The model can be seen as an extension of the wiretap II model where the adversary not only selects its view of the transmitted word, but also can erase a fraction of the codeword. eAWTP codes provide security and reliability for communication over eAWTP channels. We derive an upper bound on the rate of eAWTP codes, and give an efficient construction of a code family that achieves the bound, hence deriving secrecy capacity of the channel. We then show that the construction can also be used for AWTP channels in which instead of erasing code components, the adversary can add noise to the codeword. The construction is the only AWTP code with constant alphabet size.
{"title":"Erasure adversarial wiretap channels","authors":"P. Wang, R. Safavi-Naini, Fuchun Lin","doi":"10.1109/ALLERTON.2015.7447126","DOIUrl":"https://doi.org/10.1109/ALLERTON.2015.7447126","url":null,"abstract":"In an erasure adversarial wiretap channel (eAWTP-channel), the adversary can select a fraction ρr of the codeword to read, and a fraction ρe of the codeword to erase. The model can be seen as an extension of the wiretap II model where the adversary not only selects its view of the transmitted word, but also can erase a fraction of the codeword. eAWTP codes provide security and reliability for communication over eAWTP channels. We derive an upper bound on the rate of eAWTP codes, and give an efficient construction of a code family that achieves the bound, hence deriving secrecy capacity of the channel. We then show that the construction can also be used for AWTP channels in which instead of erasing code components, the adversary can add noise to the codeword. The construction is the only AWTP code with constant alphabet size.","PeriodicalId":112948,"journal":{"name":"2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"89 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131964487","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-09-01DOI: 10.1109/ALLERTON.2015.7447023
Qianrui Li, Paul de Kerret, D. Gesbert, N. Gresset
We consider in this work the Distributed Channel State Information (DCSI) Broadcast Channel (BC) setting, in which the various Transmitters (TXs) compute elements of the precoder based on their individual estimates of the global multiuser channel matrix. Previous works relative to the DCSI setting assume the estimation errors at different TXs to be uncorrelated, while we consider in contrast in this work that the CSI noises can be correlated. This generalization bridges the gap between the fully distributed and the centralized setting, and offers an avenue to analyze partially centralized networks. In addition, we generalize the regularized Zero Forcing (ZF) precoding by letting each TX use a different regularization coefficient. Building upon random matrix theory tools, we obtain a deterministic equivalent for the rate achieved in the large system limit from which we can optimize the regularization coefficients at different TXs. This extended precoding scheme in which each TX applies the optimal regularization coefficient is denoted as “DCSI Regularized ZF” and we show by numerical simulations that it allows to significantly reduce the negative impact of the distributed CSI configuration and is robust to the distribution of CSI quality level across all TXs.
{"title":"Robust regularized ZF in decentralized Broadcast Channel with correlated CSI noise","authors":"Qianrui Li, Paul de Kerret, D. Gesbert, N. Gresset","doi":"10.1109/ALLERTON.2015.7447023","DOIUrl":"https://doi.org/10.1109/ALLERTON.2015.7447023","url":null,"abstract":"We consider in this work the Distributed Channel State Information (DCSI) Broadcast Channel (BC) setting, in which the various Transmitters (TXs) compute elements of the precoder based on their individual estimates of the global multiuser channel matrix. Previous works relative to the DCSI setting assume the estimation errors at different TXs to be uncorrelated, while we consider in contrast in this work that the CSI noises can be correlated. This generalization bridges the gap between the fully distributed and the centralized setting, and offers an avenue to analyze partially centralized networks. In addition, we generalize the regularized Zero Forcing (ZF) precoding by letting each TX use a different regularization coefficient. Building upon random matrix theory tools, we obtain a deterministic equivalent for the rate achieved in the large system limit from which we can optimize the regularization coefficients at different TXs. This extended precoding scheme in which each TX applies the optimal regularization coefficient is denoted as “DCSI Regularized ZF” and we show by numerical simulations that it allows to significantly reduce the negative impact of the distributed CSI configuration and is robust to the distribution of CSI quality level across all TXs.","PeriodicalId":112948,"journal":{"name":"2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"143 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117334191","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-09-01DOI: 10.1109/ALLERTON.2015.7447076
M. Khabbazian
Motivated by applications to distributed storage and computing, the multi-version coding problem was formulated by Wang and Cadambe in [4]. In this problem, a client sequently over time stores v independent versions of a message in a storage system with n server nodes. It is assumed that, a message version may not reach some servers, and that each server is unaware of what has been stored in other servers. The problem requires that any c servers must be able to reconstruct their latest common version. An extended multi-version problem introduced in [5] relaxes the above requirement by requiring any c servers to be able to reconstruct their latest common version or any version later than that. The objective in both the original and extended multi-version problem is to minimize the worst case storage cost. In this work, we propose codes for both the multi-version problem and its extension. For the original multi-version coding problem, we show that the storage cost of our proposed codes are near-optimal. For the extended multi-version coding problem, we show that the storage cost of our first algorithm is optimal when v|c - 1. Our second proposed extended multi-version code shows that storage cost of strictly less than one is achievable even when v is 50% larger than c. This is interesting, as the storage cost of existing codes becomes one as soon as v becomes larger than c.
{"title":"Near-optimal multi-version codes","authors":"M. Khabbazian","doi":"10.1109/ALLERTON.2015.7447076","DOIUrl":"https://doi.org/10.1109/ALLERTON.2015.7447076","url":null,"abstract":"Motivated by applications to distributed storage and computing, the multi-version coding problem was formulated by Wang and Cadambe in [4]. In this problem, a client sequently over time stores v independent versions of a message in a storage system with n server nodes. It is assumed that, a message version may not reach some servers, and that each server is unaware of what has been stored in other servers. The problem requires that any c servers must be able to reconstruct their latest common version. An extended multi-version problem introduced in [5] relaxes the above requirement by requiring any c servers to be able to reconstruct their latest common version or any version later than that. The objective in both the original and extended multi-version problem is to minimize the worst case storage cost. In this work, we propose codes for both the multi-version problem and its extension. For the original multi-version coding problem, we show that the storage cost of our proposed codes are near-optimal. For the extended multi-version coding problem, we show that the storage cost of our first algorithm is optimal when v|c - 1. Our second proposed extended multi-version code shows that storage cost of strictly less than one is achievable even when v is 50% larger than c. This is interesting, as the storage cost of existing codes becomes one as soon as v becomes larger than c.","PeriodicalId":112948,"journal":{"name":"2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121134255","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-09-01DOI: 10.1109/ALLERTON.2015.7447164
Mina Karzand, Guy Bresler
We consider the problem of learning an Ising model for the purpose of subsequently performing inference from partial observations. This is in contrast to most other work on graphical model learning, which tries to learn the true underlying graph. This objective requires a lower bound on the strength of edges for identifiability of the model. We show that in the relatively simple case of tree models, the Chow-Liu algorithm learns a distribution with accurate low-order marginals despite the model possibly being non-identifiable. In other words, a model that appears rather different from the truth nevertheless allows to carry out inference accurately.
{"title":"Inferning trees","authors":"Mina Karzand, Guy Bresler","doi":"10.1109/ALLERTON.2015.7447164","DOIUrl":"https://doi.org/10.1109/ALLERTON.2015.7447164","url":null,"abstract":"We consider the problem of learning an Ising model for the purpose of subsequently performing inference from partial observations. This is in contrast to most other work on graphical model learning, which tries to learn the true underlying graph. This objective requires a lower bound on the strength of edges for identifiability of the model. We show that in the relatively simple case of tree models, the Chow-Liu algorithm learns a distribution with accurate low-order marginals despite the model possibly being non-identifiable. In other words, a model that appears rather different from the truth nevertheless allows to carry out inference accurately.","PeriodicalId":112948,"journal":{"name":"2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"369 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114861281","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-09-01DOI: 10.1109/ALLERTON.2015.7447052
Aftab Ahmed, Erik I. Verriest
Analysis and design of present machining methods used in mechanical engineering are based on Taylor series approximations and linearizations which cause erroneous and anomalous results. High precision machining cannot tolerate such errors. We consider and analyze an exact mathematical model of the turning process without performing any kind of linearization of the model. We give a strategic design of an estimator for the position of a machining tool based on first principles. The system's dynamics are characterized by a nonlinear State-Dependent Delay Differential Equation (SD-DDE). This delay is extremely convoluted with the state by an implicit relation. The central tenet is to use inversion of the delay model and to extract the state vector given the delay. We use our recently developed observation technique referred to as Delay Injection. Both linear asymptotic and nonlinear observers with different architectures are designed for the state estimation of a machine tool based on state-dependent delay measurement. Simulation results are depicted at the end which portray the effectiveness, validity and usefulness of the proposed observer schemes.
{"title":"Design of linear & nonlinear observers for a turning process with implicit State-Dependent Delay","authors":"Aftab Ahmed, Erik I. Verriest","doi":"10.1109/ALLERTON.2015.7447052","DOIUrl":"https://doi.org/10.1109/ALLERTON.2015.7447052","url":null,"abstract":"Analysis and design of present machining methods used in mechanical engineering are based on Taylor series approximations and linearizations which cause erroneous and anomalous results. High precision machining cannot tolerate such errors. We consider and analyze an exact mathematical model of the turning process without performing any kind of linearization of the model. We give a strategic design of an estimator for the position of a machining tool based on first principles. The system's dynamics are characterized by a nonlinear State-Dependent Delay Differential Equation (SD-DDE). This delay is extremely convoluted with the state by an implicit relation. The central tenet is to use inversion of the delay model and to extract the state vector given the delay. We use our recently developed observation technique referred to as Delay Injection. Both linear asymptotic and nonlinear observers with different architectures are designed for the state estimation of a machine tool based on state-dependent delay measurement. Simulation results are depicted at the end which portray the effectiveness, validity and usefulness of the proposed observer schemes.","PeriodicalId":112948,"journal":{"name":"2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121883845","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-09-01DOI: 10.1109/ALLERTON.2015.7447105
Vinay Praneeth Boda, P. Narayan
Consider a discrete memoryless multiple source with m component sources. A subset of k ≤ m sources are sampled at each time instant and jointly compressed in order to reconstruct all the m sources under a given distortion criterion. A sampling rate distortion function is characterized for the case of memoryless random sampling with the sampler possibly depending on the source outputs; and the decoder is informed of the sequence of sampled sets. Examining the structure of the optimal sampler, it is shown that deterministic sampling, characterized by a conditional point-mass, suffices. Restricted forms of sampling are also addressed. An upper bound for the sampling rate distortion function is provided when the decoder is not informed of the sequence of sampled sets.
{"title":"Memoryless sampling rate distortion","authors":"Vinay Praneeth Boda, P. Narayan","doi":"10.1109/ALLERTON.2015.7447105","DOIUrl":"https://doi.org/10.1109/ALLERTON.2015.7447105","url":null,"abstract":"Consider a discrete memoryless multiple source with m component sources. A subset of k ≤ m sources are sampled at each time instant and jointly compressed in order to reconstruct all the m sources under a given distortion criterion. A sampling rate distortion function is characterized for the case of memoryless random sampling with the sampler possibly depending on the source outputs; and the decoder is informed of the sequence of sampled sets. Examining the structure of the optimal sampler, it is shown that deterministic sampling, characterized by a conditional point-mass, suffices. Restricted forms of sampling are also addressed. An upper bound for the sampling rate distortion function is provided when the decoder is not informed of the sequence of sampled sets.","PeriodicalId":112948,"journal":{"name":"2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125090579","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-09-01DOI: 10.1109/ALLERTON.2015.7557347
M. Rasekh, Dongning Guo, Upamanyu Madhow
The exponential growth in demand for mobile data requires significant increases in spatial reuse, motivating an evolution towards picocellular architectures with densely deployed base stations. Providing backhaul for such a network is a key challenge, because of the high access link rates, and the cost and difficulty of running optical fiber to base stations that might be opportunistically placed on lampposts and rooftops. Wireless backhaul using millimeter (mm) wave spectrum is therefore an attractive and flexible approach, given the plentiful availability of spectrum and the possibility of synthesizing highly directive, steerable links. In this paper, we formulate and investigate the problem of joint resource allocation and routing on such a mm wave backhaul network, providing a linear programming formulation that accounts for mutual interference across simultaneously active links. While the number of variables grows exponentially in network size, it is possible to prune the problem size so that it is manageable for moderately sized networks. Numerical results and design implications are briefly discussed.
{"title":"Interference-aware routing and spectrum allocation for millimeter wave backhaul in urban picocells","authors":"M. Rasekh, Dongning Guo, Upamanyu Madhow","doi":"10.1109/ALLERTON.2015.7557347","DOIUrl":"https://doi.org/10.1109/ALLERTON.2015.7557347","url":null,"abstract":"The exponential growth in demand for mobile data requires significant increases in spatial reuse, motivating an evolution towards picocellular architectures with densely deployed base stations. Providing backhaul for such a network is a key challenge, because of the high access link rates, and the cost and difficulty of running optical fiber to base stations that might be opportunistically placed on lampposts and rooftops. Wireless backhaul using millimeter (mm) wave spectrum is therefore an attractive and flexible approach, given the plentiful availability of spectrum and the possibility of synthesizing highly directive, steerable links. In this paper, we formulate and investigate the problem of joint resource allocation and routing on such a mm wave backhaul network, providing a linear programming formulation that accounts for mutual interference across simultaneously active links. While the number of variables grows exponentially in network size, it is possible to prune the problem size so that it is manageable for moderately sized networks. Numerical results and design implications are briefly discussed.","PeriodicalId":112948,"journal":{"name":"2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127936415","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-09-01DOI: 10.1109/ALLERTON.2015.7447051
G. Kamath, K. Jagannathan, G. Raina
Reaction delays play an important role in determining the qualitative dynamical properties of a platoon of vehicles driving on a straight road. In this paper, we investigate the impact of delayed feedback on the dynamics of two widely-studied car-following models; namely, the classical car-following model and the optimal velocity model. We first conduct a control-theoretic analysis for both models and derive conditions that ensure local stability. We then demonstrate that the transition of traffic flow from the locally stable to the unstable regime occurs via a Hopf bifurcation. Qualitatively, this results in the emergence of limit cycles, which manifest as a back-propagating congestion wave. The analysis is complemented with stability charts and bifurcation diagrams. We also outline some of the implications that our results may have on the design of stable systems in the context of self-driven vehicles.
{"title":"Car-following models with delayed feedback: Local stability and Hopf bifurcation","authors":"G. Kamath, K. Jagannathan, G. Raina","doi":"10.1109/ALLERTON.2015.7447051","DOIUrl":"https://doi.org/10.1109/ALLERTON.2015.7447051","url":null,"abstract":"Reaction delays play an important role in determining the qualitative dynamical properties of a platoon of vehicles driving on a straight road. In this paper, we investigate the impact of delayed feedback on the dynamics of two widely-studied car-following models; namely, the classical car-following model and the optimal velocity model. We first conduct a control-theoretic analysis for both models and derive conditions that ensure local stability. We then demonstrate that the transition of traffic flow from the locally stable to the unstable regime occurs via a Hopf bifurcation. Qualitatively, this results in the emergence of limit cycles, which manifest as a back-propagating congestion wave. The analysis is complemented with stability charts and bifurcation diagrams. We also outline some of the implications that our results may have on the design of stable systems in the context of self-driven vehicles.","PeriodicalId":112948,"journal":{"name":"2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128365663","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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