Robust Iterative Solution of a Class of Time-Dependent Optimal Control Problems

The fast iterative solution of optimal control problems, and in particular PDE-constrained optimization problems, has become an active area of research in applied mathematics and numerical analysis. In this paper, we consider the solution of a class of time-dependent PDE-constrained optimization problems, specifically the distributed control of the heat equation. We develop a strategy to approximate the (1,1)-block and Schur complement of the saddle point system that results from solving this problem, and therefore derive a block diagonal preconditioner to be used within the MINRES algorithm. We present numerical results to demonstrate that this approach yields a robust solver with respect to step-size and regularization parameter

Fast iterative solution of reaction-diffusion control problems arising from chemical processes

PDE-constrained optimization problems, and the development of preconditioned iterative methods for the efficient solution of the arising matrix system, is a field of numerical analysis that has recently been attracting much attention. In this paper, we analyze and develop preconditioners for matrix systems that arise from the optimal control of reaction-diffusion equations, which themselves result from chemical processes. Important aspects in our solvers are saddle point theory, mass matrix representation and effective Schur complement approximation, as well as the outer (Newton) iteration to take account of the nonlinearity of the underlying PDEs

Regularization-robust preconditioners for time-dependent PDE constrained optimization problems

In this article, we motivate, derive and test �effective preconditioners to be used with the Minres algorithm for solving a number of saddle point systems, which arise in PDE constrained optimization problems. We consider the distributed control problem involving the heat equation with two diff�erent functionals, and the Neumann boundary control problem involving Poisson's equation and the heat equation. Crucial to the eff�ectiveness of our preconditioners in each case is an eff�ective approximation of the Schur complement of the matrix system. In each case, we state the problem being solved, propose the preconditioning approach, prove relevant eigenvalue bounds, and provide numerical results which demonstrate that our solvers are eff�ective for a wide range of regularization parameter values, as well as mesh sizes and time-steps

Simultaneous localisation and mapping on a multi-degree of freedom biomimetic whiskered robot

A biomimetic mobile robot called “Shrewbot” has been built as part of a neuroethological study of the mammalian facial whisker sensory system. This platform has been used to further evaluate the problem space of whisker based tactile Simultaneous Localisation And Mapping (tSLAM). Shrewbot uses a biomorphic 3-dimensional array of active whiskers and a model of action selection based on tactile sensory attention to explore a circular walled arena sparsely populated with simple geometric shapes. Datasets taken during this exploration have been used to parameterise an approach to localisation and mapping based on probabilistic occupancy grids. We present the results of this work and conclude that simultaneous localisation and mapping is possible given only noisy odometry and tactile information from a 3-dimensional array of active biomimetic whiskers and no prior information of features in the environment

Polarization Observations with the Cosmic Background Imager

We describe polarization observations of the CMBR with the Cosmic Background Imager, a 13 element interferometer which operates in the 26-36 GHz band from Llano de Chajnantour in northern Chile. The array consists of 90-cm Cassegrain antennas mounted on a steerable platform which can be rotated about the optical axis to facilitate polarization observations. The CBI employs single mode circularly polarized receivers which sample multipoles from ℓ~400 to ℓ~4250. The instrumental polarization of the CBI was calibrated with 3C279, a bright polarized point source which was monitored with the VLA

Early Scottish Monasteries and Prehistory: A Preliminary Dialogue

Reflecting oil the diversity of monastic attributes found in the east and west of Britain, the author proposes that prehistoric ritual practice was influential on monastic form. An argument is advanced that this was not based solely oil inspiration Front the landscape, nor oil conservative tradition, but oil the intellectual reconciliation of Christian and non-Christian ideas, with disparate results that account. for the differences in monumentality. Among more general matters tentatively credited with a prehistoric root are the cult of relics, the tonsure and the date of Easter

BRAHMS: Novel middleware for integrated systems computation

Biological computational modellers are becoming increasingly interested in building large, eclectic models, including components on many different computational substrates, both biological and non-biological. At the same time, the rise of the philosophy of embodied modelling is generating a need to deploy biological models as controllers for robots in real-world environments. Finally, robotics engineers are beginning to find value in seconding biomimetic control strategies for use on practical robots. Together with the ubiquitous desire to make good on past software development effort, these trends are throwing up new challenges of intellectual and technological integration (for example across scales, across disciplines, and even across time) - challenges that are unmet by existing software frameworks. Here, we outline these challenges in detail, and go on to describe a newly developed software framework, BRAHMS. that meets them. BRAHMS is a tool for integrating computational process modules into a viable, computable system: its generality and flexibility facilitate integration across barriers, such as those described above, in a coherent and effective way. We go on to describe several cases where BRAHMS has been successfully deployed in practical situations. We also show excellent performance in comparison with a monolithic development approach. Additional benefits of developing in the framework include source code self-documentation, automatic coarse-grained parallelisation, cross-language integration, data logging, performance monitoring, and will include dynamic load-balancing and 'pause and continue' execution. BRAHMS is built on the nascent, and similarly general purpose, model markup language, SystemML. This will, in future, also facilitate repeatability and accountability (same answers ten years from now), transparent automatic software distribution, and interfacing with other SystemML tools. (C) 2009 Elsevier Ltd. All rights reserved

Cerebellar-inspired algorithm for adaptive control of nonlinear dielectric elastomerbased artificial muscle

© 2016 The Author(s) Published by the Royal Society. All rights reserved. Electroactive polymer actuators are important for soft robotics, but can be difficult to control because of compliance, creep and nonlinearities. Because biological control mechanisms have evolved to deal with such problems, we investigated whether a control scheme based on the cerebellum would be useful for controlling a nonlinear dielectric elastomer actuator, a class of artificial muscle. The cerebellum was represented by the adaptive filter model, and acted in parallel with a brainstem, an approximate inverse plant model. The recurrent connections between the two allowed for direct use of sensory error to adjust motor commands. Accurate tracking of a displacement command in the actuator's nonlinear range was achieved by either semi-linear basis functions in the cerebellar model or semi-linear functions in the brainstem corresponding to recruitment in biological muscle. In addition, allowing transfer of training between cerebellum and brainstem as has been observed in the vestibulo-ocular reflex prevented the steady increase in cerebellar output otherwise required to deal with creep. The extensibility and relative simplicity of the cerebellar-based adaptive-inverse control scheme suggests that it is a plausible candidate for controlling this type of actuator. Moreover, its performance highlights important features of biological control, particularly nonlinear basis functions, recruitment and transfer of training