A digital aircraft control system can be tested exhaustively on its own, but the moment it connects to the real world—sensing wind, moving flaps—the number of possible states becomes infinite and impossible to fully check. This is the core problem CICADA tackles: hybrid systems, where a finite digital controller interacts with an infinite analogue environment. Current design methods for such systems are either trusted but conservative, or advanced but untestable. The gap is dangerous—military aircraft rely on inherently unstable designs that only digital controls can fly, yet we lack the tools to verify those controls with full confidence. The centre will bring together mathematicians, computer scientists, and control engineers to develop new modelling and testing techniques for hybrid systems. If successful, the work could make digitally controlled aircraft, autonomous vehicles, and other safety-critical systems both more advanced and more trustworthy. It will also train the next generation of researchers and create a permanent hub for collaboration between industry, where the hardest problems arise, and academia, which holds the mathematical tools to solve them.
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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.
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