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.
Organisations
Publications
Al-Mohy A
(2010)
A New Scaling and Squaring Algorithm for the Matrix Exponential
in SIAM Journal on Matrix Analysis and Applications
Al-Mohy A
(2011)
Computing the Action of the Matrix Exponential, with an Application to Exponential Integrators
in SIAM Journal on Scientific Computing
Al-Mohy A
(2012)
Improved Inverse Scaling and Squaring Algorithms for the Matrix Logarithm
in SIAM Journal on Scientific Computing
Al-Nuaimi Y
(2012)
A prototypic mathematical model of the human hair cycle.
in Journal of theoretical biology
Aprahamian M
(2014)
The Matrix Unwinding Function, with an Application to Computing the Matrix Exponential
in SIAM Journal on Matrix Analysis and Applications
Arhosalo I
(2012)
Visible parts of fractal percolation
in Proceedings of the Edinburgh Mathematical Society
Baier G
(2012)
The importance of modeling epileptic seizure dynamics as spatio-temporal patterns.
in Frontiers in physiology
Baran J
(2008)
Runtime Verification
Baran J
(2007)
Logic, Language, Information and Computation
Barringer H
(2008)
Rule Systems for Run-time Monitoring: from EAGLE to RULER
in Journal of Logic and Computation
Barringer H
(2009)
Modelling evolvable component systems: Part I: A logical framework
in Logic Journal of IGPL
Barringer H
(2007)
Runtime Verification
Barringer H
(2009)
Runtime Verification
Betcke T
(2013)
NLEVP A Collection of Nonlinear Eigenvalue Problems
in ACM Transactions on Mathematical Software
Botella-Soler V
(2012)
Emergence of hierarchical networks and polysynchronous behaviour in simple adaptive systems
in EPL (Europhysics Letters)
Botella-Soler V
(2014)
Hierarchy and polysynchrony in an adaptive network.
in Physical review. E, Statistical, nonlinear, and soft matter physics
Botella-Soler V
(2014)
Hierarchy and Polysynchrony in an adaptive network
Botella-Soler V
(2012)
Families of piecewise linear maps with constant Lyapunov exponent
Botella-Soler V
(2013)
Lyapunov exponent and topological entropy plateaus in piecewise linear maps
in Journal of Physics A: Mathematical and Theoretical
Boxall G
(2015)
Algebraic Values of Certain Analytic Functions
in International Mathematics Research Notices
Brackley CA
(2012)
A max-plus model of ribosome dynamics during mRNA translation.
in Journal of theoretical biology
Broomhead D
(2012)
Finite-dimensional behaviour and observability in a randomly forced PDE
in Dynamical Systems
Broomhead D
(2013)
Algebraic approach to time borrowing
in IET Computers & Digital Techniques
Bujorianu L
(2012)
Stochastic Reachability Analysis of Hybrid Systems
Bujorianu M
(2009)
Computational Logic in Multi-Agent Systems
Bujorianu M
(2011)
State constrained reachability for stochastic hybrid systems
in Nonlinear Analysis: Hybrid Systems
Bujorianu M
(2009)
State Constrained Reachability for Stochastic Hybrid Systems
in IFAC Proceedings Volumes
Bujorianu M
(2008)
Symmetry reduction for stochastic hybrid systems
Bujorianu M
(2011)
How good are the stochastic analysis methods for stochastic reachability
Bujorianu M
(2011)
Systems theory in an analytic setting
Bujorianu M
(2009)
Dealing with stochastic reachability
Bujorianu M
(2009)
Large deviation methods for stochastic reachability
Bujorianu M
(2009)
An Integrated Specification Logic for Cyber-Physical Systems
Bujorianu M
(2010)
Variational inequalities for the stochastic reachability problem
Butterworth J
(2009)
Stability of learning dynamics in two-agent, imperfect-information games
CERDA G
(2012)
CONTROL OF A COMPLIANT HUMANOID ROBOT IN DOUBLE SUPPORT PHASE: A GEOMETRIC APPROACH
in International Journal of Humanoid Robotics
Chahlaoui Y
(2012)
A posteriori error bounds for discrete balanced truncation
in Linear Algebra and its Applications
Chahlaoui Younes
(2011)
TWO EFFICIENT SVD/KRYLOV ALGORITHMS FOR MODEL ORDER REDUCTION OF LARGE SCALE SYSTEMS
in ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS
Dallali H
(2009)
Advances in Robotics Research
Dingle N
(2013)
Reducing the influence of tiny normwise relative errors on performance profiles
in ACM Transactions on Mathematical Software
Evatt G
(2012)
Mineral reserves under price uncertainty
in Resources Policy
Ferguson A
(2010)
The Hausdorff dimension of the projections of self-affine carpets
in Fundamenta Mathematicae
Ferguson A
(2009)
The Hausdorff dimension of the projections of self-affine carpets
Geoff Evatt
(2011)
The Resource Valuation and Optimisation Model: Real Impact from Real Options
in Application of Computers and Operational Research in the Mining Industry, Proceedings of the 35th APCOM Symposium.
GLENDINNING P
(2012)
BIFURCATIONS OF SNAP-BACK REPELLERS WITH APPLICATION TO BORDER-COLLISION BIFURCATIONS
in International Journal of Bifurcation and Chaos
Glendinning P
(2014)
Renormalization for the boundary of chaos in piecewise monotonic maps with a single discontinuity
in Nonlinearity
Glendinning P
(2012)
Universal scaling of rotation intervals for quasi-periodically forced circle maps
in Dynamical Systems
Glendinning P
(2015)
Grazing-sliding bifurcations, border collision maps and the curse of dimensionality for piecewise smooth bifurcation theory
in Nonlinearity
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 | 09/2010 |
End | 03/2012 |