scholarly journals Feedback synthesis for underactuated systems using sequential second-order needle variations

2018 ◽  
Vol 37 (13-14) ◽  
pp. 1826-1853 ◽  
Author(s):  
Giorgos Mamakoukas ◽  
Malcolm A. MacIver ◽  
Todd D. Murphey

This paper derives nonlinear feedback control synthesis for general control affine systems using second-order actions, the second-order needle variations of optimal control, as the basis for choosing each control response to the current state. A second result of this paper is that the method provably exploits the nonlinear controllability of a system by virtue of an explicit dependence of the second-order needle variation on the Lie bracket between vector fields. As a result, each control decision necessarily decreases the objective when the system is nonlinearly controllable using first-order Lie brackets. Simulation results using a differential drive cart, an underactuated kinematic vehicle in three dimensions, and an underactuated dynamic model of an underwater vehicle demonstrate that the method finds control solutions when the first-order analysis is singular. Finally, the underactuated dynamic underwater vehicle model demonstrates convergence even in the presence of a velocity field.

2021 ◽  
Vol 3 ◽  
Author(s):  
Vera Lomazzi

Although measurement invariance is widely considered a precondition for meaningful cross-sectional comparisons, substantive studies have often neglected evaluating this assumption, thereby risking drawing conclusions and making theoretical generalizations based on misleading results. This study offers a theoretical overview of the key issues concerning the measurement and the comparison of socio-political values and aims to answer the questions of what must be evaluated, why, when, and how to assess measurement equivalence. This paper discusses the implications of formative and reflective approaches to the measurement of socio-political values and introduces challenges in their comparison across different countries. From this perspective, exact and approximate approaches to equivalence are described as well as their empirical translation in statistical techniques, such as the multigroup confirmatory factor analysis (MGCFA) and the frequentist alignment method. To illustrate the application of these methods, the study investigates the construct of solidarity as measured by European Values Study (EVS) and using data collected in 34 countries in the last wave of the EVS (2017–2020). The concept is captured through a battery of nine items reflecting three dimensions of solidarity: social, local, and global. Two measurement models are hypothesized: a first-order factor model, in which the three independent dimensions of solidarity are correlated, and a second-order factor model, in which solidarity is conceived according to a hierarchical principle, and the construct of solidarity is reflected in the three sub-factors. In testing the equivalence of the first-order factor model, the results of the MGCFA indicated that metric invariance was achieved. The alignment method supported approximate equivalence only when the model was reduced to two factors, excluding global solidarity. The second-order factor model fit the data of only seven countries, in which this model could be used to study solidarity as a second-order concept. However, the comparison across countries resulted not appropriate at any level of invariance. Finally, the implications of these results for further substantive research are discussed.


2022 ◽  
Vol 12 ◽  
Author(s):  
Carolyn M. Youssef-Morgan ◽  
Llewellyn E. van Zyl ◽  
Barbara L. Ahrens

This study explores gratitude as a multidimensional and work-specific construct. Utilizing a sample of 625 employees from a variety of positions in a medium-sized school district in the United States, we developed and evaluated a new measure, namely the Work Gratitude Scale (WGS), which encompasses recognized conative (intentional), cognitive, affective, and social aspects of gratitude. A systematic, six-phased approach through structural equation modeling (SEM) was used to explore and confirm the factorial structure, internal consistency, measurement invariance, concurrent, convergent, and discriminant validity of the WGS. The results supported a 10-item measure with three dimensions: “grateful appraisals” (three items), “gratitude toward others” (four items), and “intentional attitude of gratitude” (three items). Thereafter, first-order, second-order, and bifactor confirmatory models were estimated and compared. Work gratitude was found to be best described by a second-order construct with three underlying first-order dimensions. Measurement invariance was supported in relation to gender. Concurrent validity was supported in relation to two existing dispositional gratitude scales, namely the Gratitude Questionnaire and the Gratitude, Resentment, and Appreciation Scale (GRAT). Convergent validity was supported in relation to the Core Self-Evaluations Scale (CSES) and the Psychological Capital Questionnaire. Discriminant validity was supported in relation to various demographic factors such as age, gender, occupation, and tenure. The findings support the WGS as a multidimensional measure that can be used in practice to measure overall work-related gratitude and to track the effectiveness of gratitude-related workplace interventions.


1968 ◽  
Vol 46 (15) ◽  
pp. 1725-1727 ◽  
Author(s):  
W. R. Smith ◽  
D. Henderson ◽  
J. A. Barker

The integrals which appear in the first-order term and the local compressibility approximation to the second-order term in the Barker–Henderson perturbation theory of fluids are evaluated analytically for the square-well potential in one and three dimensions and are compared with exact calculations.


1994 ◽  
Vol 03 (01) ◽  
pp. 139-144 ◽  
Author(s):  
G. BARNICH ◽  
M. HENNEAUX ◽  
R. TATAR

Recent results on the cohomological reformulation of the problem of consistent interactions between gauge fields are illustrated in the case of the Yang-Mills models. By evaluating the local BRST cohomology through descent equation techniques, it is shown (i) that there is a unique local, Poincaré invariant cubic vertex for free gauge vector fields which preserves the number of gauge symmetries to first order in the coupling constant; and (ii) that consistency to second order in the coupling constant requires the structure constants appearing in the cubic vertex to fulfill the Jacobi identity. The known uniqueness of the Yang-Mills coupling is therefore rederived through cohomological arguments.


2018 ◽  
Vol 24 (4) ◽  
pp. 289-308 ◽  
Author(s):  
Toshihiro Yamada ◽  
Kenta Yamamoto

Abstract This paper proposes a new Markov chain approach to second-order weak approximations of stochastic differential equations (SDEs) driven by d-dimensional Brownian motion. The scheme is explicitly constructed by polynomials of Brownian motions up to second order, and any discrete moment-matched random variables or the Lévy area simulation method are not used. The required number of random variables is still d in one-step simulation of the implementation of the scheme. In the Markov chain, a correction term with Lie bracket of vector fields associated with SDEs appears as the cost of not using moment-matched random variables.


Author(s):  
K. V. Polyakova

The linear frame bundle over a smooth manifold is considered. The mapping dе defined by the differentials of the first-order frame e is a lift to the normal N, i. e., a space complementing the first-order tangent space to the second-order tangent space to this bundle. In particular, the map­ping defined by the differentials of the vertical vector of this frame is a vertical lift into normal N. The lift dе allows us to construct a prolongation both of the tangent space and its vertical subspace into the second-order tangent space, more precisely into the normal N. The normal lift dе defines the normal prolon­gation of the tangent space (i. e. the normal N) and its vertical subspace. The vertical lift defines the vertical prolongation of the tangent space and its vertical subspace. The differential of an arbitrary vector field on the linear frame bundle is a complete lift from the first-order tangent space to the second-order tangent space to this bundle. It is known that the action of vector fields as differential operators on functions coincides with action of the differentials of these functions as 1-forms on these vector fields. Horizontal vectors played a dual role in the fibre bundle. On the one hand, the basic horizontal vectors serve as opera­tors for the covariant differentiation of geometric objects in the bundle. On the other hand, the differentials of these geometric objects can be con­sidered as forms (including tangential-valued ones) and their values on basic horizontal vectors give covariant derivatives of these geometric ob­jects. For objects which covariant derivatives require the second-order con­nection, the covariant derivatives are equal to the values of the differen­tials of these objects on horizontal vectors in prolonged affine connectivi­ty. Prolongations of the basic horizontal vectors, i. e., the second-order horizontal vectors for prolonged connection, were constructed. The sec­ond-order tangent space is represented as a straight sum of the first-order tangent space, vertical prolongations of the vertical and horizontal sub­spaces, and horizontal prolongation of the horizontal subspace.


Author(s):  
María Pilar Aparicio-Flores ◽  
María Vicent ◽  
Ricardo Sanmartín ◽  
Carolina Gonzálvez ◽  
Roberto Ovidio Freire-Andino ◽  
...  

Perfectionistic Automatic Thoughts (PATs) are currently being studied due to their association with maladaptive variables. This study aims to validate the Spanish version of the Perfectionism Cognitions Inventory (PCI) in a sample of Ecuadorian undergraduates as well as to analyze latent mean differences across sex. The sample was composed by 3060 undergraduates (Mage = 22.7, SD = 2.46). The Spanish model of the PCI composed by 17 items divided into three first-order dimensions (perfectionistic concerns, strivings, and demands) and a second-order factor was supported by confirmatory factor analysis. Acceptable levels of reliability and factorial invariance across sex were observed. Higher latent mean scores for males in comparison with females in the second-order factor of the PCI were found. The three dimensions of the PCI significantly and positively correlated with interpersonal difficulties. Overall, results demonstrate that the Spanish version of the PCI is a valid and reliable measure to evaluate PATs in Ecuadorian undergraduates.


1997 ◽  
Vol 36 (04/05) ◽  
pp. 315-318 ◽  
Author(s):  
K. Momose ◽  
K. Komiya ◽  
A. Uchiyama

Abstract:The relationship between chromatically modulated stimuli and visual evoked potentials (VEPs) was considered. VEPs of normal subjects elicited by chromatically modulated stimuli were measured under several color adaptations, and their binary kernels were estimated. Up to the second-order, binary kernels obtained from VEPs were so characteristic that the VEP-chromatic modulation system showed second-order nonlinearity. First-order binary kernels depended on the color of the stimulus and adaptation, whereas second-order kernels showed almost no difference. This result indicates that the waveforms of first-order binary kernels reflect perceived color (hue). This supports the suggestion that kernels of VEPs include color responses, and could be used as a probe with which to examine the color visual system.


2017 ◽  
Vol 9 (3) ◽  
pp. 17-30
Author(s):  
Kelly James Clark

In Branden Thornhill-Miller and Peter Millican’s challenging and provocative essay, we hear a considerably longer, more scholarly and less melodic rendition of John Lennon’s catchy tune—without religion, or at least without first-order supernaturalisms (the kinds of religion we find in the world), there’d be significantly less intra-group violence. First-order supernaturalist beliefs, as defined by Thornhill-Miller and Peter Millican (hereafter M&M), are “beliefs that claim unique authority for some particular religious tradition in preference to all others” (3). According to M&M, first-order supernaturalist beliefs are exclusivist, dogmatic, empirically unsupported, and irrational. Moreover, again according to M&M, we have perfectly natural explanations of the causes that underlie such beliefs (they seem to conceive of such natural explanations as debunking explanations). They then make a case for second-order supernaturalism, “which maintains that the universe in general, and the religious sensitivities of humanity in particular, have been formed by supernatural powers working through natural processes” (3). Second-order supernaturalism is a kind of theism, more closely akin to deism than, say, Christianity or Buddhism. It is, as such, universal (according to contemporary psychology of religion), empirically supported (according to philosophy in the form of the Fine-Tuning Argument), and beneficial (and so justified pragmatically). With respect to its pragmatic value, second-order supernaturalism, according to M&M, gets the good(s) of religion (cooperation, trust, etc) without its bad(s) (conflict and violence). Second-order supernaturalism is thus rational (and possibly true) and inconducive to violence. In this paper, I will examine just one small but important part of M&M’s argument: the claim that (first-order) religion is a primary motivator of violence and that its elimination would eliminate or curtail a great deal of violence in the world. Imagine, they say, no religion, too.Janusz Salamon offers a friendly extension or clarification of M&M’s second-order theism, one that I think, with emendations, has promise. He argues that the core of first-order religions, the belief that Ultimate Reality is the Ultimate Good (agatheism), is rational (agreeing that their particular claims are not) and, if widely conceded and endorsed by adherents of first-order religions, would reduce conflict in the world.While I favor the virtue of intellectual humility endorsed in both papers, I will argue contra M&M that (a) belief in first-order religion is not a primary motivator of conflict and violence (and so eliminating first-order religion won’t reduce violence). Second, partly contra Salamon, who I think is half right (but not half wrong), I will argue that (b) the religious resources for compassion can and should come from within both the particular (often exclusivist) and the universal (agatheistic) aspects of religious beliefs. Finally, I will argue that (c) both are guilty, as I am, of the philosopher’s obsession with belief. 


2009 ◽  
Vol 74 (1) ◽  
pp. 43-55 ◽  
Author(s):  
Dennis N. Kevill ◽  
Byoung-Chun Park ◽  
Jin Burm Kyong

The kinetics of nucleophilic substitution reactions of 1-(phenoxycarbonyl)pyridinium ions, prepared with the essentially non-nucleophilic/non-basic fluoroborate as the counterion, have been studied using up to 1.60 M methanol in acetonitrile as solvent and under solvolytic conditions in 2,2,2-trifluoroethan-1-ol (TFE) and its mixtures with water. Under the non- solvolytic conditions, the parent and three pyridine-ring-substituted derivatives were studied. Both second-order (first-order in methanol) and third-order (second-order in methanol) kinetic contributions were observed. In the solvolysis studies, since solvent ionizing power values were almost constant over the range of aqueous TFE studied, a Grunwald–Winstein equation treatment of the specific rates of solvolysis for the parent and the 4-methoxy derivative could be carried out in terms of variations in solvent nucleophilicity, and an appreciable sensitivity to changes in solvent nucleophilicity was found.


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