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With the increasing deployment of battery storage devices in residential electricity networks, it is essential that the charging and discharging of these devices be scheduled so as to avoid adverse impacts on the electricity distribution network. In this paper, we propose a non-cooperative, price-based hierarchical distributed optimisation approach that provably recovers the centralised, or cooperative, optimal performance from the point of view of the network operator. The distributed optimisation algorithm provides important insights into the appropriate design of contracts between an energy provider and their associated residential customers, who can themselves act as energy providers as well as consumers (e.g. due to rooftop solar photovoltaics and batteries) depending on the time of the day and on real-time prices. To make the presentation self-contained, and to highlight key properties of the price-based optimisation algorithm, the dual ascent method and its convergence properties are reviewed. The performance of the proposed price-based optimisation algorithm is validated on recent measurement taken from an Australian electricity distribution company, Ausgrid. In addition to analysing the results of the open loop solution, we investigate the effect of real-time prices in the closed loop using a model predictive control framework. [ABSTRACT FROM AUTHOR]

Systems and control theory have found wide application in the analysis and design of numerical algorithms. The authors present an equivalent discrete-time dynamical system interpretation of an algorithm commonly used in information theory called belief propagation (BP). BP is one instance of the so-called sum–product algorithm and arises, for example, in the context of iterative decoding of low-density parity-check codes. The authors review a few known results from information theory in the language of dynamical systems and show that the typically very high-dimensional, non-linear dynamical system corresponding to BP has interesting structural properties. For the linear case, they completely characterise the behaviour of this dynamical system in terms of its asymptotic input–output map. Finally, the authors state some of the open problems concerning BP in terms of the dynamical system presented. [ABSTRACT FROM AUTHOR]

A class of error correction codes called ‘low-density parity-check (LDPC)’ codes have been the subject of a great deal of recent study in the coding community as a result of their ability to approach Shannon's fundamental capacity limit. Crucial to the performance of these codes is the use of an ‘iterative’ decoder. These iterative decoders are effectively high-dimensional, nonlinear dynamical systems and, consequently, control-theoretic tools are useful in analysing such decoders. The authors describe LDPC codes and the decoding algorithm and make a connection between the fixed points of the decoding algorithm and the well-known root locus plot. Through two examples of LDPC codes, the authors show that the root locus plot visually captures the bifurcation behaviour of iterative decoding that occurs at the signal-to-noise ratio predicted by Shannon's noisy channel coding theorem. [ABSTRACT FROM AUTHOR]