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.

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.

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.

Bridge-localized HOMO-binding character of divinylanthracene-bridged dinuclear ruthenium carbonyl complexes: spectroscopic, spectroelectrochemical, and computational studies

The electronic properties of four divinylanthracene-bridged diruthenium carbonyl complexes [{RuCl(CO)(PMe3)3}2(μ[BOND]CH[DOUBLE BOND]CHArCH[DOUBLE BOND]CH)] (Ar=9,10-anthracene (1), 1,5-anthracene (2), 2,6-anthracene (3), 1,8-anthracene (4)) obtained by molecular spectroscopic methods (IR, UV/Vis/near-IR, and EPR spectroscopy) and DFT calculations are reported. IR spectroelectrochemical studies have revealed that these complexes are first oxidized at the noninnocent bridging ligand, which is in line with the very small ν(C[TRIPLE BOND]O) wavenumber shift that accompanies this process and also supported by DFT calculations. Because of poor conjugation in complex 1, except oxidized 1+, the electronic absorption spectra of complexes 2+, 3+, and 4+ all display the characteristic near-IR band envelopes that have been deconvoluted into three Gaussian sub-bands. Two of the sub-bands belong mainly to metal-to-ligand charge-transfer (MLCT) transitions according to results from time-dependent DFT calculations. EPR spectroscopy of chemically generated 1+–4+ proves largely ligand-centered spin density, again in accordance with IR spectra and DFT calculations results.

Computational fluid dynamics modelling of the air movement in an environmental test chamber with a respiring manikin

In recent years, computational fluid dynamics (CFD) has been widely used as a method of simulating airflow and addressing indoor environment problems. The complexity of airflows within the indoor environment would make experimental investigation difficult to undertake and also imposes significant challenges on turbulence modelling for flow prediction. This research examines through CFD visualization how air is distributed within a room. Measurements of air temperature and air velocity have been performed at a number of points in an environmental test chamber with a human occupant. To complement the experimental results, CFD simulations were carried out and the results enabled detailed analysis and visualization of spatial distribution of airflow patterns and the effect of different parameters to be predicted. The results demonstrate the complexity of modelling human exhalation within a ventilated enclosure and shed some light into how to achieve more realistic predictions of the airflow within an occupied enclosure.

Computational analysis of the LRRK2 interactome

LRRK2 was identified in 2004 as the causative protein product of the Parkinson’s disease locus designated PARK8. In the decade since then, genetic studies have revealed at least 6 dominant mutations in LRRK2 linked to Parkinson’s disease, alongside one associated with cancer. It is now well established that coding changes in LRRK2 are one of the most common causes of Parkinson’s. Genome-wide association studies (GWAs) have, more recently, reported single nucleotide polymorphisms (SNPs) around the LRRK2 locus to be associated with risk of developing sporadic Parkinson’s disease and inflammatory bowel disorder. The functional research that has followed these genetic breakthroughs has generated an extensive literature regarding LRRK2 pathophysiology; however, there is still no consensus as to the biological function of LRRK2. To provide insight into the aspects of cell biology that are consistently related to LRRK2 activity, we analysed the plethora of candidate LRRK2 interactors available through the BioGRID and IntAct data repositories. We then performed GO terms enrichment for the LRRK2 interactome. We found that, in two different enrichment portals, the LRRK2 interactome was associated with terms referring to transport, cellular organization, vesicles and the cytoskeleton. We also verified that 21 of the LRRK2 interactors are genetically linked to risk for Parkin- son’s disease or inflammatory bowel disorder. The implications of these findings are discussed, with particular regard to potential novel areas of investigation.

Synapses in digital medium: computational investigations of neural basis of anticipation

Anticipation is an emerging concept that can provide a bridge between the deepest philosophical theories about the nature of life and cognition on one hand and the empirical biological sciences steeped in reductionist and Newtonian conception of causality. Three conceptions of anticipation have been emerging from the literature that may be operationalised in a way leading to a viable empirical programme. The discussion of the research into a novel dynamical concept of anticipating synchronisation lends credence to such a possibility and suggests further links between the three anticipation paradigms. A careful progress mindful to the deep philosophical concerns but also respecting empirical evidence will ultimately lead towards unifying theoretical and empirical biological sciences and may offer progress where reductionist science have been so far faltering.

Molecular insights of p47phox phosphorylation dynamics in the regulation of NADPH oxidase activation and superoxide production

Phagocyte superoxide production by a multicomponent NADPH oxidase is important in host defense against microbial invasion. However inappropriate NADPH oxidase activation causes inflammation. Endothelial cells express NADPH oxidase and endothelial oxidative stress due to prolonged NADPH oxidase activation predisposes many diseases. Discovering the mechanism of NADPH oxidase activation is essential for developing novel treatment of these diseases. The p47phox is a key regulatory subunit of NADPH oxidase; however, due to the lack of full protein structural information, the mechanistic insight of p47phox phosphorylation in NADPH oxidase activation remains incomplete. Based on crystal structures of three functional domains, we generated a computational structural model of the full p47phox protein. Using a combination of in silico phosphorylation, molecular dynamics simulation and protein/protein docking, we discovered that the C-terminal tail of p47phox is critical for stabilizing its autoinhibited structure. Ser-379 phosphorylation disrupts H-bonds that link the C-terminal tail to the autoinhibitory region (AIR) and the tandem Src homology 3 (SH3) domains, allowing the AIR to undergo phosphorylation to expose the SH3 pocket for p22phox binding. These findings were confirmed by site-directed mutagenesis and gene transfection of p47phox_/_ coronary microvascular cells. Compared with wild-type p47phoxcDNAtransfected cells, the single mutation of S379A completely blocked p47phox membrane translocation, binding to p22phox and endothelial O2 . production in response to acute stimulation of PKC. p47phox C-terminal tail plays a key role in stabilizing intramolecular interactions at rest. Ser-379 phosphorylation is a molecular switch which initiates p47phox conformational changes and NADPH oxidase-dependent superoxide production by cells.