arXiv subjects

Mikael Johansson

Publications and source records attributed to Mikael Johansson.

At least 91 records · Page 5Linked to original sources

arXiv2014

Emergent Behaviors over Signed Random Dynamical Networks: State-Flipping Model

Recent studies from social, biological, and engineering network systems have drawn attention to the dynamics over signed networks, where each link is associated with a positive/negative sign indicating trustful/mistrustful, activator/inhibitor, or secure/malicious interactions. We study asymptotic dynamical patterns that emerge among a set of nodes that interact in a dynamically evolving signed random network. Node interactions take place at random on a sequence of deterministic signed graphs. Each node receives positive or negative recommendations from its neighbors depending on the sign of the interaction arcs, and updates its state accordingly. Recommendations along a positive arc follow the standard consensus update. As in the work by Altafini, negative recommendations use an update where the sign of the neighbor state is flipped. Nodes may weight positive and negative recommendations differently, and random processes are introduced to model the time-varying attention that nodes pay to these recommendations. Conditions for almost sure convergence and divergence of the node states are established. We show that under this so-called state-flipping model, all links contribute to a consensus of the absolute values of the nodes, even under switching sign patterns and dynamically changing environment. A no-survivor property is established, indicating that every node state diverges almost surely if the maximum network state diverges.

cs.SI↗

arXiv2014

Approximation of Markov Processes by Lower Dimensional Processes via Total Variation Metrics

The aim of this paper is to approximate a finite-state Markov process by another process with fewer states, called herein the approximating process. The approximation problem is formulated using two different methods. The first method, utilizes the total variation distance to discriminate the transition probabilities of a high dimensional Markov process and a reduced order Markov process. The approximation is obtained by optimizing a linear functional defined in terms of transition probabilities of the reduced order Markov process over a total variation distance constraint. The transition probabilities of the approximated Markov process are given by a water-filling solution. The second method, utilizes total variation distance to discriminate the invariant probability of a Markov process and that of the approximating process. The approximation is obtained via two alternative formulations: (a) maximizing a functional of the occupancy distribution of the Markov process, and (b) maximizing the entropy of the approximating process invariant probability. For both formulations, once the reduced invariant probability is obtained, which does not correspond to a Markov process, a further approximation by a Markov process is proposed which minimizes the Kullback-Leibler divergence. These approximations are given by water-filling solutions. Finally, the theoretical results of both methods are applied to specific examples to illustrate the methodology, and the water-filling behavior of the approximations.

math.OC↗

arXiv2014

Asymptotic Stability and Decay Rates of Homogeneous Positive Systems With Bounded and Unbounded Delays

There are several results on the stability of nonlinear positive systems in the presence of time delays. However, most of them assume that the delays are constant. This paper considers time-varying, possibly unbounded, delays and establishes asymptotic stability and bounds the decay rate of a significant class of nonlinear positive systems which includes positive linear systems as a special case. Specifically, we present a necessary and sufficient condition for delay-independent stability of continuous-time positive systems whose vector fields are cooperative and homogeneous. We show that global asymptotic stability of such systems is independent of the magnitude and variation of the time delays. For various classes of time delays, we are able to derive explicit expressions that quantify the decay rates of positive systems. We also provide the corresponding counterparts for discrete-time positive systems whose vector fields are non-decreasing and homogeneous.

eess.SY↗

arXiv2014

A Buffer-aided Successive Opportunistic Relay Selection Scheme with Power Adaptation and Inter-Relay Interference Cancellation for Cooperative Diversity Systems

In this paper we consider a simple cooperative network consisting of a source, a destination and a cluster of decode-and-forward half-duplex relays. At each time-slot, the source and (possibly) one of the relays transmit a packet to another relay and the destination, respectively, resulting in inter-relay interference (IRI). In this work, with the aid of buffers at the relays, we mitigate the detrimental effect of IRI through interference cancellation. More specifically, we propose the min-power scheme that minimizes the total energy expenditure per time slot under an IRI cancellation scheme. Apart from minimizing the energy expenditure, the min-power selection scheme, also provides better throughput and lower outage probability than existing works in the literature. It is the first time that interference cancellation is combined with buffer-aided relays and power adaptation to mitigate the IRI and minimize the energy expenditure. The new relay selection policy is analyzed in terms of outage probability and diversity, by modeling the evolution of the relay buffers as a Markov Chain (MC). We construct the state transition matrix of the MC, and hence obtain the steady state with which we can characterize the outage probability. The proposed scheme outperforms relevant state-of-the-art relay selection schemes in terms of throughput, diversity and energy efficiency, as demonstrated via examples.

cs.IT↗

arXiv2014

Sub-homogeneous positive monotone systems are insensitive to heterogeneous time-varying delays

We show that a sub-homogeneous positive monotone system with bounded heterogeneous time-varying delays is globally asymptotically stable if and only if the corresponding delay-free system is globally asymptotically stable. The proof is based on an extension of a delay-independent stability result for monotone systems under constant delays by Smith to systems with bounded heterogeneous time-varying delays. Under the additional assumption of positivity and sub-homogeneous vector fields, we establish the aforementioned delay insensitivity property and derive a novel test for global asymptotic stability. If the system has a unique equilibrium point in the positive orthant, we prove that our stability test is necessary and sufficient. Specialized to positive linear systems, our results extend and sharpen existing results from the literature.

eess.SY↗

arXiv2014

Modular design of jointly optimal controllers and forwarding policies for wireless control

We consider the joint design of packet forwarding policies and controllers for wireless control loops where sensor measurements are sent to the controller over an unreliable and energy-constrained multi-hop wireless network. For fixed sampling rate of the sensor, the co-design problem separates into two well-defined and independent subproblems: transmission scheduling for maximizing the deadline-constrained reliability and optimal control under packet loss. We develop optimal and implementable solutions for these subproblems and show that the optimally co-designed system can be efficiently found. Numerical examples highlight the many trade-offs involved and demonstrate the power of our approach.

math.OC↗

arXiv2014

Optimal parameter selection for the alternating direction method of multipliers (ADMM): quadratic problems

The alternating direction method of multipliers (ADMM) has emerged as a powerful technique for large-scale structured optimization. Despite many recent results on the convergence properties of ADMM, a quantitative characterization of the impact of the algorithm parameters on the convergence times of the method is still lacking. In this paper we find the optimal algorithm parameters that minimize the convergence factor of the ADMM iterates in the context of l2-regularized minimization and constrained quadratic programming. Numerical examples show that our parameter selection rules significantly outperform existing alternatives in the literature.

math.OC↗

arXiv2013

Exponential Stability of Homogeneous Positive Systems of Degree One With Time-Varying Delays

While the asymptotic stability of positive linear systems in the presence of bounded time delays has been thoroughly investigated, the theory for nonlinear positive systems is considerably less well-developed. This paper presents a set of conditions for establishing delay-independent stability and bounding the decay rate of a significant class of nonlinear positive systems which includes positive linear systems as a special case. Specifically, when the time delays have a known upper bound, we derive necessary and sufficient conditions for exponential stability of (a) continuous-time positive systems whose vector fields are homogeneous and cooperative, and (b) discrete-time positive systems whose vector fields are homogeneous and order preserving. We then present explicit expressions that allow us to quantify the impact of delays on the decay rate and show that the best decay rate of positive linear systems that our bounds provide can be found via convex optimization. Finally, we extend the results to general linear systems with time-varying delays.

eess.SY↗

arXiv2013

Emergent Behaviors over Signed Random Networks in Dynamical Environments

We study asymptotic dynamical patterns that emerge among a set of nodes that interact in a dynamically evolving signed random network. Node interactions take place at random on a sequence of deterministic signed graphs. Each node receives positive or negative recommendations from its neighbors depending on the sign of the interaction arcs, and updates its state accordingly. Positive recommendations follow the standard consensus update while two types of negative recommendations, each modeling a different type of antagonistic or malicious interaction, are considered. Nodes may weigh positive and negative recommendations differently, and random processes are introduced to model the time-varying attention that nodes pay to the positive and negative recommendations. Various conditions for almost sure convergence, divergence, and clustering of the node states are established. Some fundamental similarities and differences are established for the two notions of negative recommendations.

cs.SI↗

arXiv2013

Distributed Output-Feedback LQG Control with Delayed Information Sharing

This paper develops a controller synthesis method for distributed LQG control problems under output-feedback. We consider a system consisting of three interconnected linear subsystems with a delayed information sharing structure. While the state-feedback case has previously been solved, the extension to output-feedback is nontrivial as the classical separation principle fails. To find the optimal solution, the controller is decomposed into two independent components: a centralized LQG-optimal controller under delayed state observations, and a sum of correction terms based on additional local information available to decision makers. Explicit discrete-time equations are derived whose solutions are the gains of the optimal controller.

eess.SY↗

arXiv2013

Randomized Consensus with Attractive and Repulsive Links

We study convergence properties of a randomized consensus algorithm over a graph with both attractive and repulsive links. At each time instant, a node is randomly selected to interact with a random neighbor. Depending on if the link between the two nodes belongs to a given subgraph of attractive or repulsive links, the node update follows a standard attractive weighted average or a repulsive weighted average, respectively. The repulsive update has the opposite sign of the standard consensus update. In this way, it counteracts the consensus formation and can be seen as a model of link faults or malicious attacks in a communication network, or the impact of trust and antagonism in a social network. Various probabilistic convergence and divergence conditions are established. A threshold condition for the strength of the repulsive action is given for convergence in expectation: when the repulsive weight crosses this threshold value, the algorithm transits from convergence to divergence. An explicit value of the threshold is derived for classes of attractive and repulsive graphs. The results show that a single repulsive link can sometimes drastically change the behavior of the consensus algorithm. They also explicitly show how the robustness of the consensus algorithm depends on the size and other properties of the graphs.

eess.SY↗

arXiv2013

Benchmarking Practical RRM Algorithms for D2D Communications in LTE Advanced

Device-to-device (D2D) communication integrated into cellular networks is a means to take advantage of the proximity of devices and allow for reusing cellular resources and thereby to increase the user bitrates and the system capacity. However, when D2D (in the 3rd Generation Partnership Project also called Long Term Evolution (LTE) Direct) communication in cellular spectrum is supported, there is a need to revisit and modify the existing radio resource management (RRM) and power control (PC) techniques to realize the potential of the proximity and reuse gains and to limit the interference at the cellular layer. In this paper, we examine the performance of the flexible LTE PC tool box and benchmark it against a utility optimal iterative scheme. We find that the open loop PC scheme of LTE performs well for cellular users both in terms of the used transmit power levels and the achieved signal-to-interference-and-noise-ratio (SINR) distribution. However, the performance of the D2D users as well as the overall system throughput can be boosted by the utility optimal scheme, because the utility maximizing scheme takes better advantage of both the proximity and the reuse gains. Therefore, in this paper we propose a hybrid PC scheme, in which cellular users employ the open loop path compensation method of LTE, while D2D users use the utility optimizing distributed PC scheme. In order to protect the cellular layer, the hybrid scheme allows for limiting the interference caused by the D2D layer at the cost of having a small impact on the performance of the D2D layer. To ensure feasibility, we limit the number of iterations to a practically feasible level. We make the point that the hybrid scheme is not only near optimal, but it also allows for a distributed implementation for the D2D users, while preserving the LTE PC scheme for the cellular users.

cs.IT↗

arXiv2013

Deterministic and Stochastic Approaches to Supervisory Control Design for Networked Systems with Time-Varying Communication Delays

This paper proposes a supervisory control structure for networked systems with time-varying delays. The control structure, in which a supervisor triggers the most appropriate controller from a multi-controller unit, aims at improving the closed-loop performance relative to what can be obtained using a single robust controller. Our analysis considers average dwell-time switching and is based on a novel multiple Lyapunov-Krasovskii functional. We develop stability conditions that can be verified by semi-definite programming, and show that the associated state feedback synthesis problem also can be solved using convex optimization tools. Extensions of the analysis and synthesis procedures to the case when the evolution of the delay mode is described by a Markov chain are also developed. Simulations on small and large-scale networked control systems are used to illustrate the effectiveness of our approach.

eess.SY↗

arXiv2012

Accelerated Gradient Methods for Networked Optimization

We develop multi-step gradient methods for network-constrained optimization of strongly convex functions with Lipschitz-continuous gradients. Given the topology of the underlying network and bounds on the Hessian of the objective function, we determine the algorithm parameters that guarantee the fastest convergence and characterize situations when significant speed-ups can be obtained over the standard gradient method. Furthermore, we quantify how the performance of the gradient method and its accelerated counterpart are affected by uncertainty in the problem data, and conclude that in most cases our proposed method outperforms gradient descent. Finally, we apply the proposed technique to three engineering problems: resource allocation under network-wide budget constraints, distributed averaging, and Internet congestion control. In all cases, we demonstrate that our algorithm converges more rapidly than alternative algorithms reported in the literature.

math.OC↗

arXiv2012

How Agreement and Disagreement Evolve over Random Dynamic Networks

The dynamics of an agreement protocol interacting with a disagreement process over a common random network is considered. The model can represent the spreading of true and false information over a communication network, the propagation of faults in a large-scale control system, or the development of trust and mistrust in a society. At each time instance and with a given probability, a pair of network nodes are selected to interact. At random each of the nodes then updates its state towards the state of the other node (attraction), away from the other node (repulsion), or sticks to its current state (neglect). Agreement convergence and disagreement divergence results are obtained for various strengths of the updates for both symmetric and asymmetric update rules. Impossibility theorems show that a specific level of attraction is required for almost sure asymptotic agreement and a specific level of repulsion is required for almost sure asymptotic disagreement. A series of sufficient and/or necessary conditions are then established for agreement convergence or disagreement divergence. In particular, under symmetric updates, a critical convergence measure in the attraction and repulsion update strength is found, in the sense that the asymptotic property of the network state evolution transits from agreement convergence to disagreement divergence when this measure goes from negative to positive. The result can be interpreted as a tight bound on how much bad action needs to be injected in a dynamic network in order to consistently steer its overall behavior away from consensus.

cs.SI↗

arXiv2012

A Regularized Saddle-Point Algorithm for Networked Optimization with Resource Allocation Constraints

We propose a regularized saddle-point algorithm for convex networked optimization problems with resource allocation constraints. Standard distributed gradient methods suffer from slow convergence and require excessive communication when applied to problems of this type. Our approach offers an alternative way to address these problems, and ensures that each iterative update step satisfies the resource allocation constraints. We derive step-size conditions under which the distributed algorithm converges geometrically to the regularized optimal value, and show how these conditions are affected by the underlying network topology. We illustrate our method on a robotic network application example where a group of mobile agents strive to maintain a moving target in the barycenter of their positions.

eess.SY↗

arXiv2012

Ergodic Mirror Descent

We generalize stochastic subgradient descent methods to situations in which we do not receive independent samples from the distribution over which we optimize, but instead receive samples that are coupled over time. We show that as long as the source of randomness is suitably ergodic---it converges quickly enough to a stationary distribution---the method enjoys strong convergence guarantees, both in expectation and with high probability. This result has implications for stochastic optimization in high-dimensional spaces, peer-to-peer distributed optimization schemes, decision problems with dependent data, and stochastic optimization problems over combinatorial spaces.

math.OC↗

arXiv2012

Contractive Interference Functions and Rates of Convergence of Distributed Power Control Laws

The standard interference functions introduced by Yates have been very influential on the analysis and design of distributed power control laws. While powerful and versatile, the framework has some drawbacks: the existence of fixed-points has to be established separately, and no guarantees are given on the rate of convergence of the iterates. This paper introduces contractive interference functions, a slight reformulation of the standard interference functions that guarantees the existence and uniqueness of fixed-points along with linear convergence of iterates. We show that many power control laws from the literature are contractive and derive, sometimes for the first time, analytical convergence rate estimates for these algorithms. We also prove that contractive interference functions converge when executed totally asynchronously and, under the assumption that the communication delay is bounded, derive an explicit bound on the convergence time penalty due to increased delay. Finally, we demonstrate that although standard interference functions are, in general, not contractive, they are all para-contractions with respect to a certain metric. Similar results for two-sided scalable interference functions are also derived.

cs.IT↗