Constraint Satisfaction Problems (CSPs) provide a powerful framework within which to phrase many computational problems from across Computer Science. In Combinatorics they are known as Homomorphism Problems and in Databases they appear as conjunctive-query containment. CSPs manifest in Artificial Intelligence in the form of temporal and spatial reasoning, and in Computational Linguistics in the guise of tree description languages. In Computational Biology, phylogenetic reconstruction is a CSP, and in Graph Theory it known as H-colouring. We propose to study the computational complexity of CSPs given by a single constraint language that may have an infinite domain. Research into the finite-domain case is now quite advanced, yet a great many interesting problems, which may not be given as finite-domain CSPs, may be given as infinite-domain CSPs. For example, this is true for most of the CSPs associated with Artificial Intelligence and Computational Linguistics. The computational complexity of most natural finite-domain CSPs is now known, yet many interesting infinite-domain CSPs have open complexity. For example, this is true of the Max Atoms problem, very closely related to Model-checking the mu-calculus, a problem of open complexity from the Verification community. It is also true of the Concatenation problem for free algebras, a problem arising in the Rewriting community. Further, a CSP was recently given that is polynomially equivalent with the elusive problem of Integer factoring. The commonality of structure across CSPs gives hope that we might find generic methods with which to analyse the computational complexity of these diverse problems. We will work on these problems specifically, as well as seeking to map out landscapes of complexity in such areas as the following. Linear Programming. Linear program feasibility is well-known to be polynomial-time solvable, How much extra expressive power can be added to linear program feasibility while maintaining its tractability? Integer programming. Integer program feasibility is well-known to be (NP-)hard to solve. How little expressive power does one need to take away to reach tractability?

Computer simulation is sometimes described as the 'third pillar' of science, alongside experiment and theory. Computer simulations have also become essential tools to aid design and development in industry. In acoustics, computer simulations are used very widely, in such diverse applications as modelling the sound of yet-to-be-built concert halls or lecture theatres, interpreting recordings from earthquakes, predicting the noise from new train lines or motorways, improving the sound of musical instruments, treatment planning in ultrasound therapy, and enhancing images in diagnostic medical ultrasound. For most computer models based on the acoustic wave equation (a mathematical expression that describes all wave effects), it is necessary to represent the variations in the acoustic field at several points per wavelength. Think of drawing the undulations in beach sand by colouring squares on graph paper; several squares are required per undulation to capture the fact the sand rises and falls. When the domain to be simulated (concert hall, ocean, human head, etc) is many hundreds of acoustic wavelengths in size, which is often the case, the computational demands become significant. To continue the analogy, this means the graph paper - the computer memory - must be very large. In many applications, therefore it has been necessary to fall back on approximate models, which neglect important wave phenomena, such as diffraction. k-Wave is an open-source (freely available) acoustic modelling toolbox that was first written to satisfy the demand for a fast and efficient full-wave model of acoustic (ultrasonic) propagation in biological tissue, and one that is easy-to-use for people who are not computational specialists. This combination has proved highly successful, and k-Wave now has many thousands of users around the world. There are users working in biomedical ultrasound and photoacoustics, but there are also many users in other fields who have found k-Wave to be useful for their particular applications. The aim of this proposal is to re-engineer and improve k-Wave. The updated code will use new programming features and software-engineering best-practices that have developed since k-Wave was first released. We will add exciting new features, such as the ability to couple acoustic and thermal models together, to make rapid predictions when the acoustic source has only a small range of frequencies, and to accurately represent complex boundaries such as those encountered in a concert hall. One major advancement will be the ability to automatically find the gradient of the solver with respect to the parameters in the wave equation. This will allow k-Wave to be directly used for applications in machine learning (deep learning, artificial intelligence). As part of the project, we will also develop new training materials, run training courses, and work with new user communities across all areas of acoustics. The proposed changes to k-Wave will not only support and improve existing simulation activities, but will spur researchers to test new ideas and exploit the new functionality in novel ways and in novel situations. The possibilities opened up by the combination of classical simulation and deep learning is particularly exciting. Potential applications include planning for ground-breaking ultrasound treatments for cancer and neurological disorders, providing a greater understanding of our ocean environments, and improving the design of acoustic spaces including opera houses and urban environments.

This proposal is concerned with the hardware acceleration of iterative numerical algorithms, with a focus on model predictive control implementations. Such model predictive controllers typically require the solution of a quadratic progamming problem every sample period. The solution of the quadratic programming problem typically requires several multidimensional Newton optimizations, each of which requires the solution of many systems of linear equations. Thus the lessons learned will be applicable to a wide class of numerical algorithms arising in practical problems within and beyond Control.The main adventurous feature of the approach from the digital electronics perspective is the potential to use Control and Systems theory to inform one of the central design problems in custom reconfigurable computing: efficient silicon utilization through appropriate finite precision number representation. In sequential (single core) computer architecture, questions of numerical precision have, by and large, been answered through the introduction of area costly high-precision IEEE compliant arithmetic units. In modern computing systems, whether FPGA-based or manycore, attention is now turning to how to make the most effective use of the silicon available for computation and, in this context, questions of numerical accuracy requirements are arising once more.The proposed approach forms a radical departure from standard industrial and academic practice in both model predictive control (MPC) and digital electronics. The main adventurous feature of the approach from the end-user perspective is the utilization of reconfigurable hardware devices, namely Field-Programmable Gate Arrays (FPGAs), to implement model predictive controllers operating at high sample rates, allowing MPC to be utilized in application areas where the computational load has been considered too great until now, such as spacecraft, aeroplanes, uninhabited autonomous vehicles, automobile control systems and gas turbines. From the theoretical perspective, the main adventure in Control is in the development of novel formulations that explcitly take advantage of parallel computational architectures.The development of a methodology to tackle this problem will involve highly novel research areas resulting from the application of control theoretic ideas to hardware development, as well as the application of hardware implementation methodologies to control system design. In particular, this proposal is the first to investigate massively parallel real-time numerical optimization on FPGAs, the first to apply control-theoretic techniques to determine appropriate number systems in custom hardware designs, and the first to study the tradeoff between circuit parallelism and numerical accuracy within a closed-loop behavioural context.As a result, this proposal directly falls within the scope of EPSRC's recently signposted Microelectronics Grand Challenge 3 - Moore for Less.

Abstracts are not currently available in GtR for all funded research. This is normally because the abstract was not required at the time of proposal submission, but may be because it included sensitive information such as personal details.

The emerging theory of negative imaginary systems is attracting increasing interest amongst control systems researchers because it captures a wide range of practical problems. Negative imaginary dynamics often arise as a simple fundamental consequence of Newton's second law of motion. Often control systems performance can be significantly improved, despite demanding robustness requirements and difficult dynamics, by directly exploiting system properties. The study of negative imaginary systems can lead to potential improvements in several engineering fields including areas of advanced technology such as nano-positioning systems, control of multi-agent dynamical systems, distributed network control, mechatronics and robotics among others. This work will develop new results in the theory of negative imaginary systems. These results will underpin controller design methods and controller tuning guidelines for this class of systems. The developed methodologies will be applied to several specific benchmark applications and case studies. Wide dissemination of the advantages of the negative imaginary concepts will be a key aspect of this work.