High-gain PI-like control of Euler–Lagrange mechanical systems: Simulations and experiments in 2DoF robotic manipulators

Euler–Lagrange mechanical systems usually possess nonlinear models, which are subject to uncertainties and unknown disturbances. In this article, a robust but smooth controller is proposed, relying on a high-gain proportional–integral structure that renders an accurate tracking, even in the case of uncertain effects. The tracking performance can be improved by adjusting a single parameter, deriving into a prescribed stability regime, where the tracking errors are locally uniformly ultimately bounded, and where the controller depends on a change of coordinates that integrates the proportional, integral, and derivative information of the tracking error. The advantages of this proposal become evident without considering an intricate implementation procedure. Numerical results are provided to highlight the reliability of the proposed method.

Randomized Simplicial Hessian Update

Recently, a derivative-free optimization algorithm was proposed that utilizes a minimum Frobenius norm (MFN) Hessian update for estimating the second derivative information, which in turn is used for accelerating the search. The proposed update formula relies only on computed function values and is a closed-form expression for a special case of a more general approach first published by Powell. This paper analyzes the convergence of the proposed update formula under the assumption that the points from Rn where the function value is known are random. The analysis assumes that the N+2 points used by the update formula are obtained by adding N+1 vectors to a central point. The vectors are obtained by transforming a prototype set of N+1 vectors with a random orthogonal matrix from the Haar measure. The prototype set must positively span a N≤n dimensional subspace. Because the update is random by nature we can estimate a lower bound on the expected improvement of the approximate Hessian. This lower bound was derived for a special case of the proposed update by Leventhal and Lewis. We generalize their result and show that the amount of improvement greatly depends on N as well as the choice of the vectors in the prototype set. The obtained result is then used for analyzing the performance of the update based on various commonly used prototype sets. One of the results obtained by this analysis states that a regular n-simplex is a bad choice for a prototype set because it does not guarantee any improvement of the approximate Hessian.

THEORETICAL DIMENSION OF INFORMATION-DIGITAL ECONOMY: INFORMATION-DIGITAL PROCESSES AND THEIR ATTRIBUTES

Cognitive activity and its types (sensory-emotional, empirical-abstract, theoretical-abstract, applied and integral-synthetic) are presented as a contradictory unity of discretizing and cretinizing components. The accompanying information-digital discretizing activity and the accompanying information-digital cretizing activity are characterized as components of the accompanying information-digital activity, their separate attributes, and also results are the basic kinds of discrete-digital materialized derivative information products. The main serial-parallel technical, technological and technical-technological processes of processing accompanying information-digital activity are considered: i) transformation of a discrete materialized derivative information product into a discrete-digital materialized derivative information product by digitization in an analog-to-digital converter; ii) own production of discrete-digital materialized derivative information products with the use of discrete-digital electronic computer; iii) conversion of a discrete-digital materialized derivative information product into an analog materialized derivative information product in a digital-to-analog converter. The composition of the knowledge-information chain of intermediate links between the real object and its final-surface designation is determined: “Real object – knowledge product – knowledge-information product – knowledge-concept product – primary information product – derivative information product – materialized derivative information product – discrete materialized derivative information product – discrete-digital materialized derivative information product.”Four types of information-digital economy are highlighted. Its core, or information-digital economy of the I kind, is represented exclusively by the accompanying information-digital activity, its types and attributes. Information-digital economy of the II kind includes information-digital economy of the I kind and production of attributes of accompanying information-digital activity both within the information economy, and outside it. Information-digital economy of the II kind together with information and non-information economic activity, the attributes of which are discrete-digital materialized derivative information products, forms the information-digital economy of the III kind. Finally, in the information-digital economy of the IV kind, along with the information-digital economy of the III kind, the components of all types of economic activity are presented, in which at least one of the attributes of the accompanying information-digital activity is used.

An Optimal High-Order Tensor Method for Convex Optimization

This paper is concerned with finding an optimal algorithm for minimizing a composite convex objective function. The basic setting is that the objective is the sum of two convex functions: the first function is smooth with up to the dth-order derivative information available, and the second function is possibly nonsmooth, but its proximal tensor mappings can be computed approximately in an efficient manner. The problem is to find—in that setting—the best possible (optimal) iteration complexity for convex optimization. Along that line, for the smooth case (without the second nonsmooth part in the objective), Nesterov proposed an optimal algorithm for the first-order methods ([Formula: see text]) with iteration complexity [Formula: see text], whereas high-order tensor algorithms (using up to general dth-order tensor information) with iteration complexity [Formula: see text] were recently established. In this paper, we propose a new high-order tensor algorithm for the general composite case, with the iteration complexity of [Formula: see text], which matches the lower bound for the dth-order methods as previously established and hence is optimal. Our approach is based on the accelerated hybrid proximal extragradient (A-HPE) framework proposed by Monteiro and Svaiter, where a bisection procedure is installed for each A-HPE iteration. At each bisection step, a proximal tensor subproblem is approximately solved, and the total number of bisection steps per A-HPE iteration is shown to be bounded by a logarithmic factor in the precision required.

Analytical first derivatives of the direct Hermite-Simpson collocation formulation of optimal control problems

In order to assess the capabilities of South Africa as a launch site for commercial satellites, an optimal control solver was developed. The developed solver makes use of direct Hermite-Simpson collocation methods, and can be applied to a general optimal control problem. Analytical first derivative information was obtained for direct Hermite-Simpson collocation methods. Typically, a numerical estimate of the derivative information is used. This paper will present the solver algorithm, and the formulation and derivation of the analytical first derivative information for this approach. A sample problem is provided as validation of the solver.

The Effectiveness of Contemporary Islamic Scholars in Tackling Pornography Addiction: A Case of Muslim Students in Britain

In the contemporary era, fatwas mostly contain derivative information from classical texts such as the Quran and Hadith. Fatwas are used to tackle pornography addiction while it may lack productivity in spreading innovative solutions among Muslim students. Failure to provide solid Islamic pornography rehabilitations and disfavouring to speak openly on pornography does not stop the prevalence of pornography among Muslim students. Therefore, the purpose is to explore the prevalence of pornography, its effect on Muslim students, and strategies to overcome pornography addiction. Through SPSS analysis, the numerical data shows that both Muslim male and female students view pornography regardless of its prohibitions. Some Muslim students are engaged in maladaptive behavior, affecting their spirituality, religion, and overall well-being (Ademola, 2017). The study, therefore, suggests alternative awareness programs to support Muslim students to overcome the struggles of pornographic addiction that is often too tempting to resist. Dealing with pornography per today's context perhaps will diminish the statistical rate of Muslim students watching pornography.

An efficient variance-based global sensitivity index based on C-DRM and Taylor expansion

Sensitivity analysis plays an important role in quantifying the impact of input uncertainty on model response uncertainty. Through sensitivity analysis, we can grasp the crucial parameters and gain a deeper understanding of the model behavior. In this paper, an effective analytical solution for solving the variance-based global sensitivity index is proposed. Firstly, the original performance function is approximated as the sum of a series of univariate functions using the conventional dimensional reduction method (C-DRM). Then, the Taylor series expansion is used to expand the univariate function as unary linear function and unary quadratic functions. Finally, the analytical solutions of the variance-based global sensitivity index based on unary linear function and unary quadratic functions are derived respectively. The computational cost of the proposed method is completely concentrated on the calculation of the partial derivative information of the performance function with respect to each variable. As long as the partial derivative information is obtained, the variance-based global sensitivity index can be obtained directly by the proposed method without any additional computational cost. For simple explicit performance functions, the derivative information can be directly derived analytically. For complex explicit or implicit performance functions, the derivative information can be estimated by some simple numerical difference methods. Five examples are studied to investigate the accuracy and efficiency of the proposed method.