The Manchester Centre for Interdisciplinary Computational and Dynamical Analysis (CICADA)

Lead Research Organisation: University of Manchester
Department Name: Mathematics

Abstract

It is said that we live in a digital age. The availability of cheap, reliable microprocessors and dense, high-speed memory has led to the mass reduction of analogue information about the real world to strings of digits which can be processed rapidly and stored without error. For most people the most obvious manifestation of this is seen in the entertainment industry. Music, for instance, can be stored digitally on a cd or an iPod, copied without degradation, and can be bought and sold electronically. Less obviously, perhaps, we rely on digital systems in circumstances where failure might result in loss of life. Military aircraft are designed for manoeuvrability by making them inherently unstable. No human pilot could fly such an aircraft without the aid of an active fly-by-wire/generally digital/control system. Commercial airlines also operate fly-by-wire aircraft, mostly digitally controlled. However, in this case there is a major gap between designs we would trust with our lives and those based on the most technically advanced solutions. We have little confidence in the latter due to their complexity and the lack of appropriate testing tools.As a general issue, whenever an embedded computer system, such as would be found in a digital controller, has to interact with the real world, we have what is known as a hybrid system. The difficulties associated with modelling and testing such systems arise because of the fundamental difference between analogue and digital systems. A digital system is finite in the sense that it is, at least in principle, possible to list/and therefore to test/all of the states it can be be found in. When a digital system begins to interact with the real world this is no longer the case and so new techniques must be devised that will allow us to predict the behaviour and test the designs of hybrid systems. The Manchester Centre for Interdisciplinary Computational and Dynamical Analysis (CICADA) will be an internationally-known centre which will bring together mathematicians, computer scientists and control theory engineers to work on this difficult, but deeply interesting and vital area. The Centre will attract internationally renowned scientists working in this field, and create a focus for research activity and, in addition, training for the next generation. A feature of the Centre will be the way it works by fostering a strong interaction between industry/where many of the hard problems are brought into sharpest focus/and academia/which has a wide range of new mathematical and computational techniques which can be brought to bear.

Publications

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Al-Mohy A (2012) Improved Inverse Scaling and Squaring Algorithms for the Matrix Logarithm in SIAM Journal on Scientific Computing

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Al-Mohy A (2010) A New Scaling and Squaring Algorithm for the Matrix Exponential in SIAM Journal on Matrix Analysis and Applications

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Al-Nuaimi Y (2012) A prototypic mathematical model of the human hair cycle. in Journal of theoretical biology

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Aprahamian M (2014) The Matrix Unwinding Function, with an Application to Computing the Matrix Exponential in SIAM Journal on Matrix Analysis and Applications

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Arhosalo I (2012) Visible parts of fractal percolation in Proceedings of the Edinburgh Mathematical Society

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Baran J (2008) Runtime Verification

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Barringer H (2008) Rule Systems for Run-time Monitoring: from EAGLE to RULER in Journal of Logic and Computation

 
Description It is impossible to do justice to the full range of research carried out, but here are some highlights. Bujorianu produced the first book on the reachability problem for stochastic hybrid systems. This book brings together the theory (Markov processes etc) necessary to deal with one of the fundamental problems in computer science. Korovina extended the systems for which rigorous computer verification is possible. Brown and Dallali looked at the interaction between discrete and continuous dynamics in robotics. The work was largely applied to the iCub and CoMan, two humanoid robots which
are being developed at the IIT, Genoa. The work investigated the interplay between different (discrete) phases of
locomotion, such as single support and double support and the transition between them which is modelled as an impacting
system (heel strike). Detailed dynamic models were built in Robotran and these models were used to design constrained
controllers and validated on simple test problems. Glendinning and Kowalczyk advanced the description of the dynamics of
hybrid systems and, with Nordmark (Sweden) and Jeffreys (Bath) made significant progress on the understanding of the
extra complexity introduced by higher dimensional settings. Conversely, Brooke, Chahlaoui and Higham worked on reducing dimensions, with Chahlaoui providing numerical methods for dimensional reduction of hybrid systems and error
bounds for these methods. Broomhead, Furber, Hook, Johnson and Kambites collaborated on different aspects of maxplus
algebras. As the trend in digital electronics proceeds to yet greater densities, design methods which allow for device
variability are needed. The max-plus time borrowing algorithms we have developed have potential application in design tools to meet this new challenge. Wong applied hybrid control in the paper industry. Mixing the expertise of the non-smooth dynamics group and the robotics group created new activity in the understanding of human balance, leading to on-going collaborations with physiologists (Loram, MMU).
Exploitation Route The max-plus expertise developed during the project led to a CICADA PhD student (Hook) moving into the Numerical Analysis group, where novel applications of max-plus algebra for high-dimensional eigenvalue problems have been developed. We expect this impact to continue. The overarching themes (reachability, piecewise smooth dynamics) and application to computer safety analysis and mechanics. Models of human balance continue to be explored using similar models (the ex-CICADA post-doc Kowalczyk receieved an EPSRC first grant to investigate this further). Dallali continues to expand the possible movement of robots.
Sectors Digital/Communication/Information Technologies (including Software),Healthcare

 
Description Cross-discip Feas 2010 1F1541
Amount £201,875 (GBP)
Funding ID EP/I016643/1 
Organisation Engineering and Physical Sciences Research Council (EPSRC) 
Sector Public
Country United Kingdom
Start 10/2010 
End 03/2012