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Zappavigna A.,Polytechnic of Milan | Charalambous T.,University of Cyprus | Knorn F.,Hamilton Institute
Automatica | Year: 2012

In this note we prove the unconditional stability of the FoschiniMiljanic algorithm. Our results show that the FoschiniMiljanic algorithm is unconditionally stable (convergent) even in the presence of bounded time-varying communication delays, and in the presence of topology changes. The implication of our results may be important for the design of Code Division Multiple Access (CDMA) based wireless networks. © 2011 Elsevier Ltd. All rights reserved.

Subramanian V.G.,Hamilton Institute | Berry R.A.,Northwestern University | Agrawal R.,Motorola Inc.
IEEE Transactions on Information Theory | Year: 2010

In this paper, the scheduling and resource allocation problem for the downlink in a code-division multiple access (CDMA)-based wireless network is considered. The problem is to select a subset of the users for transmission and for each of the users selected, to choose the modulation and coding scheme, transmission power, and number of codes used. We refer to this combination as the physical layer operating point (PLOP). Each PLOP consumes different amounts of code and power resources. The resource allocation task is to pick the optimal PLOP taking into account both system-wide and individual user resource constraints that can arise in a practical system. This problem is tackled as part of a utility maximization problem framed in earlier papers that includes both scheduling and resource allocation. In this setting, the problem reduces to maximizing the weighted throughput over the state-dependent downlink capacity region while taking into account the system-wide and individual user constraints. This problem is studied for the downlink of a Gaussian broadcast channel with orthogonal CDMA transmissions. This results in a tractable convex optimization problem. A dual formulation is used to obtain several key structural properties. By exploiting this structure, algorithms are developed to find the optimal solution with geometric convergence. © 2010 IEEE.

Middleton R.H.,Hamilton Institute | Braslavsky J.H.,University of Newcastle
IEEE Transactions on Automatic Control | Year: 2010

This paper gives sufficient conditions for string instability in an array of linear time-invariant autonomous vehicles with communication constraints. The vehicles are controlled autonomously and are subject to a rigid or semi-rigid formation policy. The individual controllers are assumed to have a limited range of forward and backward communication with other vehicles. Sufficient conditions are given that imply a lower bound on the peak of the frequency response magnitude of the transfer function mapping a disturbance to the leading vehicle to a vehicle in the chain. This lower bound quantifies the effect of spacing separation policy, intervehicle communication policy, and vehicle settling response performance. These results extend earlier works to give a unified treatment of heterogeneous, non-nearest neighbor communication and semi-rigid one-dimensional formation control. © 2006 IEEE.

Leith D.J.,Hamilton Institute | Cao Q.,Hamilton Institute | Subramanian V.G.,Northwestern University
IEEE/ACM Transactions on Networking | Year: 2012

In this paper, we establish that the rate region of a large class of IEEE 802.11 mesh networks is log-convex, immediately allowing standard utility fairness methods to be generalized to this class of networks. This creates a solid theoretical underpinning for fairness analysis and resource allocation in this practically important class of networks. For the special case of max-min fairness, we use this new insight to obtain an almost complete characterization of the fair rate allocation and a remarkably simple, practically implementable method for achieving max-min fairness in 802.11 mesh networks. © 2012 IEEE.

Corless M.,Purdue University | Shorten R.,Hamilton Institute
Automatica | Year: 2011

Systems and control theory has long been a rich source of problems for the numerical linear algebra community. In many problems, conditions on analytic functions of a complex variable are usually evaluated by solving a special generalized eigenvalue problem. In this paper we develop a general framework for studying such problems. We show that for these problems, solutions can be obtained by either solving a generalized eigenvalue problem, or by solving an equivalent eigenvalue problem. A consequence of this observation is that these problems can always be solved by finding the eigenvalues of a Hamiltonian (or discrete-time counterpart) matrix, even in cases where an associated Hamiltonian matrix, cannot (normally) be defined. We also derive a number of new compact tests for determining whether or not a transfer function matrix is strictly positive real. These tests, which are of independent interest due to the fact that many problems can be recast as SPR problems, are defined even in the case when the matrix D+D* is singular, and can be formulated without requiring inversion of the system matrix A. © 2010 Elsevier Ltd. All rights reserved.

Corless M.,Purdue University | Shorten R.,Hamilton Institute
IEEE Transactions on Automatic Control | Year: 2010

We present conditions which are necessary and sufficient for a transfer function (or transfer function matrix) to be strictly positive real. A counter-example is given to illustrate that the conditions presented here differ from those previously presented in the literature. The proof of our results differs from previous related proofs in that it only uses properties of analytic functions and matrices and does not require state-space realizations. Also, the results are not restricted to rational transfer functions with real coefficients. © 2010 IEEE.

Stanojevic R.,Telefonica | Shorten R.,Hamilton Institute
Proceedings - IEEE INFOCOM | Year: 2010

In recent years we have witnessed a great interest in large distributed computing platforms, also known as clouds. While these systems offer enormous computing power, they are major energy consumers. In existing data centers CPUs are responsible for approximately half of the energy consumed by the servers. A promising technique for saving CPU energy consumption is dynamic speed scaling, in which the speed at which the processor is run is adjusted based on demand and performance constraints. In this paper we look at the problem of allocating the demand in the network of processors (each being capable to perform dynamic speed scaling) to minimize the global energy consumption/cost subject to a performance constraint. The nonlinear dependence between the energy consumption and the performance as well as the high variability in the energy prices result in a nontrivial resource allocation. The problem can be abstracted as a fully distributed convex optimization with a linear constraint. On the theoretical side, we propose two low-overhead fully decentralized algorithms for solving the problem of interest and provide closed-form conditions that ensure stability of the algorithms. Then we evaluate the efficacy of the optimal solution using simulations driven by the real-world energy prices. Our findings indicate a possible cost reduction of 10- 40% compared to power-oblivious 1/N load balancing, for a wide range of load factors. ©2010 IEEE.

Narendra K.S.,Yale University | Shorten R.,Hamilton Institute
IEEE Transactions on Automatic Control | Year: 2010

In this note, a simple method is presented that is both necessary and sufficient for determining whether a given Metzler matrix $A$ is Hurwitz. The method is based on the well known fact that a Hurwitz Metzler matrix is also diagonally stable. By using this fact, very simple conditions are derived for the Hurwitz stability of a Metzler matrix. The conditions are stated in terms of the signs of the diagonal entries of a sequence of lower dimensional matrices. The efficacy of the conditions is demonstrated by applying them to determine stability in several examples. © 2006 IEEE.

Huang K.D.,Hamilton Institute | Malone D.,Hamilton Institute | Duffy K.R.,Hamilton Institute
IEEE Transactions on Wireless Communications | Year: 2011

The robustness to noise of the 802.11b/g 5.5 Mb/s and 11 Mb/s rates must be investigated experimentally as they cannot be predicted theoretically. In this paper we report on detailed outdoor and indoor measurements that lead us to the surprising conclusion that the 11 Mb/s 802.11g rate experiences fewer packet losses than the 6 Mb/s 802.11g rate at any given (symbol) SNR. This occurs due to the combination of modulation and physical layer coding schemes used by these rates and has serious implications for rate control algorithms. The practical implications of this, factoring in the interaction between packet loss and 802.11 MAC retries, is that 6 Mb/s is effectively redundant as a packet transmission rate if the 11 Mb/s rate is available. © 2011 IEEE.

Wellstead P.,Hamilton Institute | Cloutier M.,Hamilton Institute
Wiley Interdisciplinary Reviews: Systems Biology and Medicine | Year: 2011

The cause of Parkinson's disease (PD) remains unknown despite it being the second most prevalent neurodegenerative condition. Indeed, there is a growing consensus that there is no single cause, and that PD is a multifactorial systemic condition, in which a number of factors may determine its etiopathogenesis. We describe a systems approach that addresses the multifactorial aspects of PD and overcomes constraints on conventional experimentation imposed by PD's causal complexity, its long temporal duration, and its uniqueness to human brains. Specifically, a mathematical model of brain energy metabolism is used as a core module to which other modules describing cellular processes thought to be associated with PD can be attached and studied in an integrative environment. Employing brain energy usage as the core of a systems approach also enables the potential role that compromised energy metabolism may have in the etiology of PD. Although developed for PD, it has not escaped our attention that the energy systems approach outlined here could also be applied to other neurodegenerative disorders-most notably Alzheimer's disease. © 2010 John Wiley & Sons, Inc.

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