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Pacifici V.,Linnaeus Center | Dan G.,Linnaeus Center
IEEE Journal on Selected Areas in Communications | Year: 2012

As a model of distributed resource allocation in networked systems, we consider resource allocation games played over a influence graph. The influence graph models limited interaction between the players due to, e.g., the network topology: the payoff that an allocated resource yields to a player depends only on the resources allocated by her neighbors on the graph. We prove that pure strategy Nash equilibria (NE) always exist in graphical resource allocation games and we provide a linear time algorithm to compute equilibria. We show that these games do not admit a potential function: if there are closed paths in the influence graph then there can be best reply cycles. Nevertheless, we show that from any initial allocation of a resource allocation game it is possible to reach a NE by playing best replies and we provide a bound on the maximal number of update steps required. Furthermore we give sufficient conditions in terms of the influence graph topology and the utility structure under which best reply cycles do not exist. Finally we propose an efficient distributed algorithm to reach an equilibrium over an arbitrary graph and we illustrate its performance on different random graph topologies. © 2012 IEEE.

Shi G.,Linnaeus Center | Johansson K.H.,Linnaeus Center
Automatica | Year: 2012

In this paper, we formulate and solve a randomized optimal consensus problem for multi-agent systems with stochastically time-varying interconnection topology. The considered multi-agent system with a simple randomized iterating rule achieves an almost sure consensus meanwhile solving the optimization problem minz∈Rd∑i=1nfi(z), in which the optimal solution set of objective function fi can only be observed by agent i itself. At each time step, simply determined by a Bernoulli trial, each agent independently and randomly chooses either taking an average among its neighbor set, or projecting onto the optimal solution set of its own optimization component. Both directed and bidirectional communication graphs are studied. Connectivity conditions are proposed to guarantee an optimal consensus almost surely with proper convexity and intersection assumptions. The convergence analysis is carried out using convex analysis. We compare the randomized algorithm with the deterministic one via a numerical example. The results illustrate that a group of autonomous agents can reach an optimal opinion by each node simply making a randomized trade-off between following its neighbors or sticking to its own opinion at each time step. © 2012 Elsevier Ltd. All rights reserved.

Negusse S.,Linnaeus Center | Handel P.,Linnaeus Center | Zetterberg P.,Linnaeus Center
Conference Record - IEEE Instrumentation and Measurement Technology Conference | Year: 2013

In this paper, theoretical properties of a maximum-likelihood (ML) estimator of signal-to-noise ratio (SNR) is discussed. The three-paremter sine fit algorithm is employed on a finite and coherently sampled measurement set corrupted by additive white Gaussian noise. Under the Gaussian noise model, the least squares solution provided by the three-parameter sine fit is also ML estimator. Exact distribution and finite sample properties of the SNR estimate are derived. Moreover, an explicit expression for the mean squared error (MSE) of the estimator is given. Simulation results are shown to verify the underlying theoretical results. © 2013 IEEE.

Singh A.,Eurecom | Elia P.,Eurecom | Jalden J.,Linnaeus Center
IEEE International Symposium on Information Theory - Proceedings | Year: 2013

Recent work in [1]-[3] quantified, in the form of a complexity exponent, the computational resources required for ML and lattice sphere decoding to achieve a certain diversity-multiplexing performance. For a specific family of layered lattice designs, and a specific set of decoding orderings, this complexity was shown to be an exponential function in the number of codeword bits, and was shown to meet a universal upper bound on complexity exponents. The same results raised the question of whether complexity reductions away from the universal upper bound are feasible, for example, with a proper choice of decoder (ML vs lattice), or with a proper choice of lattice codes and decoding ordering policies. The current work addresses this question by first showing that for almost any full-rate DMT optimal lattice code, there exists no decoding ordering policy that can reduce the complexity exponent of ML or lattice based sphere decoding away from the universal upper bound, i.e., that a randomly picked lattice code (randomly and uniformly drawn from an ensemble of DMT optimal lattice designs) will almost surely be such that no decoding ordering policy can provide exponential complexity reductions away from the universal upper bound. As a byproduct of this, the current work proves the fact that ML and (MMSE-preprocessed) lattice decoding share the same complexity exponent for a very broad setting, which now includes almost any DMT optimal code (again randomly drawn) and all decoding order policies. Under a basic richness of codes assumption, this is in fact further extended to hold, with probability one, over all full-rate codes. Under the same assumption, the result allows for a meaningful rate-reliability-complexity tradeoff that holds, almost surely in the random choice of the full-rate lattice design, and which holds irrespective of the decoding ordering policy. This tradeoff can be used to, for example, describe the optimal achievable diversity gain of ML or lattice sphere decoding in the presence of limited computational resources. © 2013 IEEE.

Parisio A.,Linnaeus Center | Rikos E.,Center for Renewable Energy Sources, Greece | Glielmo L.,Universitadegli Studi Del Sannio
IEEE Transactions on Control Systems Technology | Year: 2014

Microgrids are subsystems of the distribution grid, which comprises generation capacities, storage devices, and controllable loads, operating as a single controllable system either connected or isolated from the utility grid. In this paper, we present a study on applying a model predictive control approach to the problem of efficiently optimizing microgrid operations while satisfying a time-varying request and operation constraints. The overall problem is formulated using mixed-integer linear programming (MILP), which can be solved in an efficient way by using commercial solvers without resorting to complex heuristics or decompositions techniques. Then, the MILP formulation leads to significant improvements in solution quality and computational burden. A case study of a microgrid is employed to assess the performance of the online optimization-based control strategy and the simulation results are discussed. The method is applied to an experimental microgrid located in Athens, Greece. The experimental results show the feasibility and the effectiveness of the proposed approach. © 1993-2012 IEEE.

Sandberg H.,Linnaeus Center | Hagg P.,Linnaeus Center | Wahlberg B.,Linnaeus Center
Systems and Control Letters | Year: 2014

This letter considers how to approximately reconstruct a cascade system from a given unstructured system estimate. Many system identification methods, including subspace methods, provide reliable but generally unstructured black-box models. The problem we consider is how to find cascade systems that are close to such black-box models. For this, we use model matching techniques and optimal weighted Hankel-norm approximation to obtain accurate low-order cascade systems. We show that it is possible to bound the reconstruction error in terms of an error tolerance parameter and weighted Hankel singular values. The suggested methods are illustrated on both a numerical example and a real double tank system with experimental data. © 2014 Elsevier B.V. All rights reserved.

Larsson C.A.,Linnaeus Center | Hagg P.,Linnaeus Center | Hjalmarsson H.,Linnaeus Center
International Journal of Adaptive Control and Signal Processing | Year: 2016

This contribution considers the problem of realizing an input signal with a desired autocorrelation sequence satisfying both input and output constraints for the system it is to be applied to. This is an important problem in system identification, firstly, because the quality and accuracy of the identified model are highly dependent on the excitation signal used during the experiment and secondly, because on real processes, it is often important to constrain the input and output of the process because of actuator saturation and safety considerations. The signal generation is formulated as a model predictive controller with probabilistic constraints to make the algorithm robust to model uncertainties and process noise. The corresponding optimization problem is then solved with tools from scenario-based stochastic optimization. To reduce the model uncertainties, the method is made adaptive where a new model of the system and its uncertainties are reidentified. The algorithm is successfully applied to a simulation example and in a practical experiment for the identification of a quadruple tank lab process. Copyright © 2015 John Wiley & Sons, Ltd.

Hadjicostis C.N.,University of Cyprus | Hadjicostis C.N.,University of Illinois at Urbana - Champaign | Charalambous T.,Linnaeus Center
IEEE Transactions on Automatic Control | Year: 2014

Classical distributed algorithms for asymptotic average consensus typically assume timely and reliable exchange of information between neighboring components of a given multi-component system. These assumptions are not necessarily valid in practice due to varying delays that might affect computations at different nodes and/or transmissions at different links. In this work, we propose a protocol that overcomes this limitation and, unlike existing consensus protocols in the presence of delays, ensures asymptotic consensus to the exact average, despite the presence of arbitrary (but bounded) delays in the communication links. The protocol requires that each component has knowledge of the number of its out-neighbors (i.e., the number of components to which it can send information) and its proof of correctness relies on the weak convergence of a backward product of column stochastic matrices. The proposed algorithm is demonstrated via illustrative examples. © 2014 IEEE.

Feyzmahdavian H.R.,Linnaeus Center | Charalambous T.,Linnaeus Center | Johansson M.,Linnaeus Center
IEEE Transactions on Automatic Control | Year: 2014

This paper develops a comprehensive stability analysis framework for general classes of continuous-time power control algorithms under heterogeneous time-varying delays. Our first set of results establish global asymptotic stability of power control laws involving two-sided scalable interference functions, and include earlier work on standard interference functions as a special case. We then consider contractive interference functions and demonstrate that the associated continuous-time power control laws always have unique fixed points which are exponentially stable, even under bounded heterogeneous time-varying delays. For this class of interference functions, we present explicit bounds on the decay rate that allow us to quantify the impact of delays on the convergence time of the algorithm. When interference functions are linear, we also prove that contractivity is necessary and sufficient for exponential stability of continuous-time power control algorithms with time-varying delays. Finally, numerical simulations illustrate the validity of our theoretical results. © 1963-2012 IEEE.

Trnka P.,Honeywell | Sturk C.,Linnaeus Center | Sandberg H.,Linnaeus Center | Havlena V.,Honeywell | And 3 more authors.
IEEE Transactions on Control Systems Technology | Year: 2013

Parallel working units in closed-loop operation are frequently encountered in industrial applications of advanced process control (boilers, turbines, chemical reactors, etc.). Control strategies typically require different low-order models for each configuration of parallel units. These different models are usually obtained by heuristics applied to the parallel models. To replace these heuristics, this paper proposes a systematic solution based on structured model order reduction. Two methods are considered, the first has general applicability to stable closed-loop systems, but gives no a priori error bounds; the second linear matrix inequality (LMI)-based method comes with an explicit error bounds, but cannot be applied to general models. However, it is shown that for models composed of cascades of stable subsystems and negative feedbacks of strictly positive real subsystems, the LMIs are always feasible. Both methods are demonstrated on a practical example of a cogeneration power plant with multiple boilers. It is proved that the second LMI-based method can always be applied to general problems with structures similar to the boiler-header systems considered in this paper. © 1993-2012 IEEE.

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