A tutorial on pseudospectral methods for computational optimal control

[English] This paper is a tutorial introduction to pseudospectral optimal control. With pseudospectral methods, a function is approximated as a linear combination of smooth basis functions, which are often chosen to be Legendre or Chebyshev polynomials. Collocation of the differential-algebraic equations is performed at orthogonal collocation points, which are selected to yield interpolation of high accuracy. Pseudospectral methods directly discretize the original optimal control problem to recast it into a nonlinear programming format. A numerical optimizer is then employed to find approximate local optimal solutions. The paper also briefly describes the functionality and implementation of PSOPT, an open source software package written in C++ that employs pseudospectral discretization methods to solve multi-phase optimal control problems. The software implements the Legendre and Chebyshev pseudospectral methods, and it has useful features such as automatic differentiation, sparsity detection, and automatic scaling. The use of pseudospectral methods is illustrated in two problems taken from the literature on computational optimal control. [Portuguese] Este artigo e um tutorial introdutorio sobre controle otimo pseudo-espectral. Em metodos pseudo-espectrais, uma funcao e aproximada como uma combinacao linear de funcoes de base suaves, tipicamente escolhidas como polinomios de Legendre ou Chebyshev. A colocacao de equacoes algebrico-diferenciais e realizada em pontos de colocacao ortogonal, que sao selecionados de modo a minimizar o erro de interpolacao. Metodos pseudoespectrais discretizam o problema de controle otimo original de modo a converte-lo em um problema de programa cao nao-linear. Um otimizador numerico e entao empregado para obter solucoes localmente otimas. Este artigo tambem descreve sucintamente a funcionalidade e a implementacao de um pacote computacional de codigo aberto escrito em C++ chamado PSOPT. Tal pacote emprega metodos de discretizacao pseudo-spectrais para resolver problemas de controle otimo com multiplas fase. O PSOPT permite a utilizacao de metodos de Legendre ou Chebyshev, e possui caractersticas uteis tais como diferenciacao automatica, deteccao de esparsidade e escalonamento automatico. O uso de metodos pseudo-espectrais e ilustrado em dois problemas retirados da literatura de controle otimo computacional.

Comments, with reply, on "Computational algorithms for pole assignment" by N.K. Nichols

Some points of the paper by N.K. Nichols (see ibid., vol.AC-31, p.643-5, 1986), concerning the robust pole assignment of linear multiinput systems, are clarified. It is stressed that the minimization of the condition number of the closed-loop eigenvector matrix does not necessarily lead to robustness of the pole assignment. It is shown why the computational method, which Nichols claims is robust, is in fact numerically unstable with respect to the determination of the gain matrix. In replying, Nichols presents arguments to support the choice of the conditioning of the closed-loop poles as a measure of robustness and to show that the methods of J Kautsky, N. K. Nichols and P. VanDooren (1985) are stable in the sense that they produce accurate solutions to well-conditioned problems.

On computational algorithms for pole assignment

A number of computationally reliable direct methods for pole assignment by feedback have recently been developed. These direct procedures do not necessarily produce robust solutions to the problem, however, in the sense that the assigned poles are insensitive to perturbalions in the closed-loop system. This difficulty is illustrated here with results from a recent algorithm presented in this TRANSACTIONS and its causes are examined. A measure of robustness is described, and techniques for testing and improving robustness are indicated.

Modular non-computational-connectionist-hybrid neural network approach to robotic systems

Spiking neural networks are usually limited in their applications due to their complex mathematical models and the lack of intuitive learning algorithms. In this paper, a simpler, novel neural network derived from a leaky integrate and fire neuron model, the ‘cavalcade’ neuron, is presented. A simulation for the neural network has been developed and two basic learning algorithms implemented within the environment. These algorithms successfully learn some basic temporal and instantaneous problems. Inspiration for neural network structures from these experiments are then taken and applied to process sensor information so as to successfully control a mobile robot.

Controlling the computational modes of the arbitrarily structured C-grid

The arbitrarily structured C-grid, TRiSK (Thuburn, Ringler, Skamarock and Klemp, 2009, 2010) is being used in the ``Model for Prediction Across Scales'' (MPAS) and is being considered by the UK Met Office for their next dynamical core. However the hexagonal C-grid supports a branch of spurious Rossby modes which lead to erroneous grid-scale oscillations of potential vorticity (PV). It is shown how these modes can be harmlessly controlled by using upwind-biased interpolation schemes for PV. A number of existing advection schemes for PV are tested, including that used in MPAS, and none are found to give adequate results for all grids and all cases. Therefore a new scheme is proposed; continuous, linear-upwind stabilised transport (CLUST), a blend between centred and linear-upwind with the blend dependent on the flow direction with respect to the cell edge. A diagnostic of grid-scale oscillations is proposed which gives further discrimination between schemes than using potential enstrophy alone and indeed some schemes are found to destroy potential enstrophy while grid-scale oscillations grow. CLUST performs well on hexagonal-icosahedral grids and unrotated skipped latitude-longitude grids of the sphere for various shallow water test cases. Despite the computational modes, the hexagonal icosahedral grid performs well since these modes are easy and harmless to filter. As a result TRiSK appears to perform better than a spectral shallow water model.

Sleepwalking certainties: agency, aesthetics, and incapacity in W.G. Sebald’s 'Austerlitz' and Hermann Broch’s 'The Sleepwalkers'

When we first encounter the narrator of Austerlitz, he is wandering around the unfamiliar town of Antwerp with, he tells us, “unsicheren Schritten” (1; 9). As well as reflecting the unfamiliarity of the locale, these “uncertain steps” evince a proud modesty characteristic of the classic Sebaldian narrator, a wanderer who discreetly relays the stories of the people and places he is privileged to encounter. Although Sebald does not use the phrase, steps of this sort, unpurposed yet unerring, are made with what is commonly known in German as somnambule Sicherheit: the legendary surefootedness of the sleepwalker. The convergence of sleepwalking and certainty in a single phrase poses an interesting challenge to one of the central tenets of the English-language canonization of Sebald, for his writing has been most highly valued for its ability to move the reader through apparent certainties towards a salutary uncertainty. But somnambule Sicherheit also presents the possibility that the current may be reversed, that narrative may move under cover of uncertainty towards certainty. That Sebald criticism has not been more troubled by this possibility is in no small part due to the fact that it tends to deploy the notion of sleepwalking with a minimum of reflection on its theoretical ramifications. To evoke some of the complexities of this matter, I first offer a brief cultural history of sleepwalking, as well as a brief account of the topic of uncertainty in Sebald criticism. Most of my argument, however, involves an extended comparative analysis of sleepwalking in Sebald's Austerlitz and Hermann Broch's 1933 trilogy The Sleepwalkers. Although these writers have not previously been the object of any sustained comparison, sleepwalking in Broch's novels illuminates much that is left implicit on the topic in Sebald's fiction and points toward some difficult questions regarding the role of aesthetics and agency in Sebald's work.

Winckelmann and the invention of antiquity: history and aesthetics in the age of Altertumswissenschaft

This volume provides a new perspective on the emergence of the modern study of antiquity, Altertumswissenschaft, in eighteenth-century Germany through an exploration of debates that arose over the work of the art historian Johann Joachim Winckelmann between his death in 1768 and the end of the century. This period has long been recognised as particularly formative for the development of modern classical studies, and over the past few decades has received increased attention from historians of scholarship and of ideas. Winckelmann's eloquent articulation of the cultural and aesthetic value of studying the ancient Greeks, his adumbration of a new method for studying ancient artworks, and his provision of a model of cultural-historical development in terms of a succession of period styles, influenced both the public and intra-disciplinary self-image of classics long into the twentieth century. Yet this area of Winckelmann's Nachleben has received relatively little attention compared with the proliferation of studies concerning his importance for late eighteenth-century German art and literature, for historians of sexuality, and his traditional status as a 'founder figure' within the academic disciplines of classical archaeology and the history of art. Harloe restores the figure of Winckelmann to classicists' understanding of the history of their own discipline and uses debates between important figures, such as Christian Gottlob Heyne, Friedrich August Wolf, and Johann Gottfried Herder, to cast fresh light upon the emergence of the modern paradigm of classics as Altertumswissenschaft: the multi-disciplinary, comprehensive, and historicizing study of the ancient world.

Solvent-dependent modulation of metal–metal electronic interactions in a dinuclear cyanoruthenate complex: a detailed electrochemical, spectroscopic and computational study

The dinuclear complex [{Ru(CN)4}2(μ-bppz)]4− shows a strongly solvent-dependent metal–metal electronic interaction which allows the mixed-valence state to be switched from class 2 to class 3 by changing solvent from water to CH2Cl2. In CH2Cl2 the separation between the successive Ru(II)/Ru(III) redox couples is 350 mVand the IVCT band (from the UV/Vis/NIR spectroelectrochemistry) is characteristic of a borderline class II/III or class III mixed valence state. In water, the redox separation is only 110 mVand the much broader IVCT transition is characteristic of a class II mixed-valence state. This is consistent with the observation that raising and lowering the energy of the d(π) orbitals in CH2Cl2 or water, respectively, will decrease or increase the energy gap to the LUMO of the bppz bridging ligand, which provides the delocalisation pathway via electron-transfer. IR spectroelectrochemistry could only be carried out successfully in CH2Cl2 and revealed class III mixed-valence behaviour on the fast IR timescale. In contrast to this, time-resolved IR spectroscopy showed that the MLCTexcited state, which is formulated as RuIII(bppz˙−)RuII and can therefore be considered as a mixed-valence Ru(II)/Ru(III) complex with an intermediate bridging radical anion ligand, is localised on the IR timescale with spectroscopically distinct Ru(II) and Ru(III) termini. This is because the necessary electron-transfer via the bppz ligand is more difficult because of the additional electron on bppz˙− which raises the orbital through which electron exchange occurs in energy. DFT calculations reproduce the electronic spectra of the complex in all three Ru(II)/Ru(II), Ru(II)/Ru(III) and Ru(III)/Ru(III) calculations in both water and CH2Cl2 well as long as an explicit allowance is made for the presence of water molecules hydrogen-bonded to the cyanides in the model used. They also reproduce the excited-state IR spectra of both [Ru(CN)4(μ-bppz)]2– and [{Ru(CN)4}2(μ-bppz)]4− very well in both solvents. The reorganization of the water solvent shell indicates a possible dynamical reason for the longer life time of the triplet state in water compared to CH2Cl2.

Postmodernism, culture and feminism: the aesthetics of space and performance in Rock Follies and Rock Follies of '77

This article discusses the aesthetic and spatial representational strategies of the popular studio-based musical television drama serials Rock Follies and Rock Follies of ’77. It analyses how the texts’ themes relating to women and the entertainment industry are mediated through their postmodern ironic mode and representation of fantastic spaces. Rock Follies’ distinctive stylised aesthetic and mode of caricature are analysed with reference to the visual intentions and ‘voice’ of the writer, Howard Schuman. Through considering the programmes’ various spatial strategies, the article draws attention to the importance of visual and performance style in their postmodern discourse on culture, fantasy, gender and subjectivity. Analysis of the spaces of musical performance, characters’ domestic environments and simulated entertainment spaces reveals how a dialectic is established between the escapist imaginative pleasures of fantasy and the manipulative and exploitative practices of the culture industry. The shift from the optimism of the first series, when the LittleLadies first form, to the darker mood of the second series, in which they are increasingly divided by industry pressures, is traced through changes in the aesthetics of space and characterisation. As a space of artifice, performance and electronic visual manipulation that facilitates the texts’ reflexive representation of culture and feminised fantasy, the studio’s unique aesthetic strengths emerge through this case study.

Dinitrogen release from arylpentazole: A picosecond time-resolved infrared, spectroelectrochemical, and DFT computational study

p-(Dimethylamino)phenyl pentazole, DMAP-N5 (DMAP = Me2N−C6H4), was characterized by picosecond transient infrared spectroscopy and infrared spectroelectrochemistry. Femtosecond laser excitation at 310 or 330 nm produces the DMAP-N5 (S1) excited state, part of which returns to the ground state (τ = 82 ± 4 ps), while DMAP-N and DMAP-N3 (S0) are generated as double and single N2-loss photoproducts with η ≈ 0.14. The lifetime of DMAP-N5 (S1) is temperature and solvent dependent. [DMAP-N3]+ is produced from DMAP-N5 in a quasireversible, one-electron oxidation process (E1/2 = +0.67 V). Control experiments with DMAP-N3 support the findings. DFT B3LYP/6-311G** calculations were used to identify DMAP-N5 (S1), DMAP-N3 +, and DMAP-N in the infrared spectra. Both DMAP-N5 (S1) and [DMAP-N5]+ have a weakened N5 ring structure.