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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]

We consider the design and control problem of concentric tubes used in stereotactic neurosurgery. The goal is to optimally reach a configuration of the cannula linking an entry point on the skullcap to a pre-specified region inside the brain. Key issues related to this task are the mechanical behaviour of the cannula and the topography of the brain. We formulate an optimal control problem in order to determine a feasible path while minimizing brain damage caused by missing follow-the-leader behaviour. Numerical results show the potential of the proposed approach. [ABSTRACT FROM AUTHOR]