We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

Networked control systems (NCSs) are spatially distributed systems for which the communication between sensors, actuators, and controllers is supported by a shared communication network. We review several recent results on estimation, analysis, and controller synthesis for NCSs. The results surveyed address channel limitations in terms of packet-rates, sampling, network delay, and packet dropouts. The results are presented in a tutorial fashion, comparing alternative methodologies

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A Survey of Recent Results in Networked Control Systems

In this note, we revisit the problem of scheduling stabilizing control tasks on embedded processors. We start from the paradigm that a real-time scheduler could be regarded as a feedback controller that decides which task is executed at any given instant. This controller has for objective guaranteeing that (control unrelated) software tasks meet their deadlines and that stabilizing control tasks asymptotically stabilize the plant. We investigate a simple event-triggered scheduler based on this feedback paradigm and show how it leads to guaranteed performance thus relaxing the more traditional periodic execution requirements.

/pdf/event-triggered-real-time-scheduling-of-stabilizing-control-t1gebqsndp.pdf

Event-Triggered Real-Time Scheduling of Stabilizing Control Tasks

This comprehensive treatment of network information theory and its applications provides the first unified coverage of both classical and recent results. With an approach that balances the introduction of new models and new coding techniques, readers are guided through Shannon's point-to-point information theory, single-hop networks, multihop networks, and extensions to distributed computing, secrecy, wireless communication, and networking. Elementary mathematical tools and techniques are used throughout, requiring only basic knowledge of probability, whilst unified proofs of coding theorems are based on a few simple lemmas, making the text accessible to newcomers. Key topics covered include successive cancellation and superposition coding, MIMO wireless communication, network coding, and cooperative relaying. Also covered are feedback and interactive communication, capacity approximations and scaling laws, and asynchronous and random access channels. This book is ideal for use in the classroom, for self-study, and as a reference for researchers and engineers in industry and academia.

Network Information Theory

Information Theory and Reliable Communication

We show that the coarsest, or least dense, quantizer that quadratically stabilizes a single input linear discrete time invariant system is logarithmic, and can be computed by solving a special linear quadratic regulator problem. We provide a closed form for the optimal logarithmic base exclusively in terms of the unstable eigenvalues of the system. We show how to design quantized state-feedback controllers, and quantized state estimators. This leads to the design of hybrid output feedback controllers. The theory is then extended to sampling and quantization of continuous time linear systems sampled at constant time intervals. We generalize the definition of density of quantization to the density of sampling and quantization in a natural way, and search for the coarsest sampling and quantization scheme that ensures stability. Finally, by relaxing the definition of quadratic stability, we show how to construct logarithmic quantizers with only finite number of quantization levels and still achieve practical stability of the closed-loop system.

/pdf/stabilization-of-linear-systems-with-limited-information-5aovy386zu.pdf

Stabilization of linear systems with limited information

Remote stabilization over fading channels

In this paper, we want to study how natural and engineered systems could perform complex optimizations with limited computational and communication capabilities. We adopt a continuous-time dynamical system view rooted in early work on optimization and more recently in network protocol design, and merge it with the dynamic view of distributed averaging systems. We obtain a general approach, based on the control system viewpoint, that allows to analyze and design (distributed) optimization systems converging to the solution of given convex optimization problems. The control system viewpoint provides many insights and new directions of research. We apply the framework to a distributed optimal location problem and demonstrate the natural tracking and adaptation capabilities of the system to changing constraints.

/pdf/a-control-perspective-for-centralized-and-distributed-convex-2terimb7sr.pdf

A control perspective for centralized and distributed convex optimization

In this paper, we show a general equivalence between feedback stabilization through an analog communication channel, and a communication scheme based on feedback which is a generalization of that of Schalkwijk and Kailath. We also show that the achievable transmission rate of the scheme is given by the Bode's sensitivity integral formula, which characterizes a fundamental limitation of causal feedback. Therefore, we can now use the many results and design tools from control theory to design feedback communication schemes providing desired communication rates, and to generate lower bounds on the channel feedback capacity. We consider single user Gaussian channels with memory and memory-less multiuser broadcast, multiple access, and interference channels. In all cases, the results we obtain either achieve the feedback capacity, when this is known, recover known best rates, or provide new best achievable rates.

When bode meets shannon: control-oriented feedback communication schemes

"Writing on dirty paper" refers to the communication problem over a channel with both noise and interference, where the interference is known to the encoder non-causally and unknown to the decoder. This problem is regarded as a basic building block in communication, and it has been extensively investigated by Costa and other researchers. However, little is known in the case that the encoder can have access to feedback from the decoder. In this paper, we study the dirty paper coding problem for feedback Gaussian channels without or with memory. We provide the most power efficient coding schemes for this problem, i.e., the schemes achieve lossless interference cancellation. These schemes are based on the Kalman filtering algorithm, extend the Schalkwijk-Kailath feedback codes, have low complexity and a doubly exponential reliability function, and reveal the interconnections among information, control, and estimation over dirty paper channels with feedback. This research may be found useful to, for example, power-constrained sensor network communication

/pdf/writing-on-dirty-paper-with-feedback-571pkg10t5.pdf

Nicola Elia

Papers

Stabilization of linear systems with limited information

Remote stabilization over fading channels

A control perspective for centralized and distributed convex optimization

When bode meets shannon: control-oriented feedback communication schemes

Writing on Dirty Paper with Feedback