Reinforcement learning based adaptive control for uncertain mechanical systems with asymptotic tracking

This paper mainly focuses on the development of a learning-based controller for a class of uncertain mechanical systems modeled by the Euler-Lagrange formulation.The considered system can depict the behavior of a large class of engineering systems,such as vehicular systems,robot manipulators and satellites.All these systems are often characterized by highly nonlinear characteristics,heavy modeling uncertainties and unknown perturbations,therefore,accurate-model-based nonlinear control approaches become unavailable.Motivated by the challenge,a reinforcement learning(RL)adaptive control methodology based on the actor-critic framework is investigated to compensate the uncertain mechanical dynamics.The approximation inaccuracies caused by RL and the exogenous unknown disturbances are circumvented via a continuous robust integral of the sign of the error(RISE)control approach.Different from a classical RISE control law,a tanh(·)function is utilized instead of a sign(·)function to acquire a more smooth control signal.The developed controller requires very little prior knowledge of the dynamic model,is robust to unknown dynamics and exogenous disturbances,and can achieve asymptotic output tracking.Eventually,co-simulations through ADAMS and MATLAB/Simulink on a three degrees-of-freedom(3-DOF)manipulator and experiments on a real-time electromechanical servo system are performed to verify the performance of the proposed approach.

Modeling Method of C/C-ZrC Composites and Prediction of Equivalent Thermal Conductivity Tensor Based on Asymptotic Homogenization

This article proposes a modeling method for C/C-ZrC composite materials.According to the superposition of Gaussian random field,the original gray model is obtained,and the threshold segmentation method is used to generate the C-ZrC inclusion model.Finally,the fiber structure is added to construct the microstructure of the three-phase plain weave composite.The reconstructed inclusions can meet the randomness of the shape and have a uniform distribution.Using an algorithm based on asymptotic homogenization and finite element method,the equivalent thermal conductivity prediction of the microstructure finite element model was carried out,and the influence of component volume fraction on material thermal properties was explored.The sensitivity of model parameters was studied,including the size,mesh sensitivity,Gaussian complexity,and correlation length of the RVE model,and the optimal calculation model was selected.The results indicate that the volume fraction of the inclusion phase has a significant impact on the equivalent thermal conductivity of the material.As the volume fraction of carbon fiber and ZrC increases,the equivalent thermal conductivity tensor gradually decreases.This model can be used to explore the impact of materialmicrostructure on the results,and numerical simulations have studied the relationship between structure and performance,providing the possibility of designing microstructure based on performance.

Asymptotic normality of error density estimator in stationary and explosive autoregressive models

In this paper,we consider the limit distribution of the error density function estima-tor in the rst-order autoregressive models with negatively associated and positively associated random errors.Under mild regularity assumptions,some asymptotic normality results of the residual density estimator are obtained when the autoregressive models are stationary process and explosive process.In order to illustrate these results,some simulations such as con dence intervals and mean integrated square errors are provided in this paper.It shows that the residual density estimator can replace the density\estimator"which contains errors.

THE LOGARITHMIC SOBOLEV INEQUALITY FOR A SUBMANIFOLD IN MANIFOLDS WITH ASYMPTOTICALLY NONNEGATIVE SECTIONAL CURVATURE

In this note,we prove a logarithmic Sobolev inequality which holds for compact submanifolds without a boundary in manifolds with asymptotically nonnegative sectional curvature.Like the Michale-Simon Sobolev inequality,this inequality contains a term involving the mean curvature.

THE ASYMPTOTIC BEHAVIOR AND OSCILLATION FOR A CLASS OF THIRD-ORDER NONLINEAR DELAY DYNAMIC EQUATIONS

In this paper,we consider a class of third-order nonlinear delay dynamic equations.First,we establish a Kiguradze-type lemma and some useful estimates.Second,we give a sufficient and necessary condition for the existence of eventually positive solutions having upper bounds and tending to zero.Third,we obtain new oscillation criteria by employing the Potzsche chain rule.Then,using the generalized Riccati transformation technique and averaging method,we establish the Philos-type oscillation criteria.Surprisingly,the integral value of the Philos-type oscillation criteria,which guarantees that all unbounded solutions oscillate,is greater than θ_(4)(t_(1),T).The results of Theorem 3.5 and Remark 3.6 are novel.Finally,we offer four examples to illustrate our results.

Enhanced Differentiable Architecture Search Based on Asymptotic Regularization

In differentiable search architecture search methods,a more efficient search space design can significantly improve the performance of the searched architecture,thus requiring people to carefully define the search space with different complexity according to various operations.Meanwhile rationalizing the search strategies to explore the well-defined search space will further improve the speed and efficiency of architecture search.With this in mind,we propose a faster and more efficient differentiable architecture search method,AllegroNAS.Firstly,we introduce a more efficient search space enriched by the introduction of two redefined convolution modules.Secondly,we utilize a more efficient architectural parameter regularization method,mitigating the overfitting problem during the search process and reducing the error brought about by gradient approximation.Meanwhile,we introduce a natural exponential cosine annealing method to make the learning rate of the neural network training process more suitable for the search procedure.Moreover,group convolution and data augmentation are employed to reduce the computational cost.Finally,through extensive experiments on several public datasets,we demonstrate that our method can more swiftly search for better-performing neural network architectures in a more efficient search space,thus validating the effectiveness of our approach.

Asymptotic behaviour of solution for fourth order wave equation with dispersive and dissipative terms

This paper studies the initial boundary value problem of fourth order wave equation with dispersive and dissipative terms. By using multiplier method, it is proven that the global strong solution of the problem decays to zero exponentially as the time approaches infinite, under a very simple and mild assumption regarding the nonlinear term.

Asymptotic Approximations of Apostol-Tangent Polynomials in Terms of Hyperbolic Functions

The tangent polynomials Tn(z)are generalization of tangent numbers or the Euler zigzag numbers Tn.In particular,Tn(0)=Tn.These polynomials are closely related to Bernoulli,Euler and Genocchi polynomials.One of the extensions and analogues of special polynomials that attract the attention of several mathematicians is the Apostol-type polynomials.One of these Apostol-type polynomials is the Apostol-tangent polynomials Tn(z,λ).Whenλ=1,Tn(z,1)=Tn(z).The use of hyperbolic functions to derive asymptotic approximations of polynomials together with saddle point method was applied to the Bernoulli and Euler polynomials by Lopez and Temme.The same method was applied to the Genocchi polynomials by Corcino et al.The essential steps in applying the method are(1)to obtain the integral representation of the polynomials under study using their exponential generating functions and the Cauchy integral formula,and(2)to apply the saddle point method.It is found out that the method is applicable to Apostol-tangent polynomials.As a result,asymptotic approximation of Apostol-tangent polynomials in terms of hyperbolic functions are derived for large values of the parameter n and uniform approximation with enlarged region of validity are also obtained.Moreover,higher-order Apostol-tangent polynomials are introduced.Using the same method,asymptotic approximation of higherorder Apostol-tangent polynomials in terms of hyperbolic functions are derived and uniform approximation with enlarged region of validity are also obtained.It is important to note that the consideration of Apostol-type polynomials and higher order Apostol-type polynomials were not done by Lopez and Temme.This part is first done in this paper.The accuracy of the approximations are illustrated by plotting the graphs of the exact values of the Apostol-tangent and higher-order Apostol-tangent polynomials and their corresponding approximate values for specific values of the parameters n,λand m.

Distributed Adaptive Asymptotic Tracking of 2-D Vehicular Platoon Systems With Actuator Faults and Spacing Constraints

Dear Editor,This letter investigates the adaptive asymptotic tracking slidingmode control for nonlinear 2-D vehicular platoon systems subject to actuator faults.Firstly,by using the Nussbaum function,the disadvantageous factors brought by the unknown direction actuator faults can be attenuated.

The Stochastic Asymptotic Stability Analysis in Two Species Lotka-Volterra Model

The asymptotic stability of two species stochastic Lotka-Volterra model is explored in this paper. Firstly, the Lotka-Volterra model with random parameter is built and reduced into the equivalent deterministic system by orthogonal polynomial approximation. Then, the linear stability theory and Routh-Hurwitz criterion for nonlinear deterministic systems are applied to the equivalent one. At last, at the aid of Lyapunov second method, we obtain that as the random intensity or statistical parameter of random variable is changed, the stability about stochastic Lotka-Volterra model is different from the deterministic system.

Asymptotic Consistency of the James-Stein Shrinkage Estimator

The study explores the asymptotic consistency of the James-Stein shrinkage estimator obtained by shrinking a maximum likelihood estimator. We use Hansen’s approach to show that the James-Stein shrinkage estimator converges asymptotically to some multivariate normal distribution with shrinkage effect values. We establish that the rate of convergence is of order and rate , hence the James-Stein shrinkage estimator is -consistent. Then visualise its consistency by studying the asymptotic behaviour using simulating plots in R for the mean squared error of the maximum likelihood estimator and the shrinkage estimator. The latter graphically shows lower mean squared error as compared to that of the maximum likelihood estimator.

On the Asymptotic Stability of Discrete Crocodilians Model

The sex ratio of crocodiles is strongly biased towards females, often as high as 10 females to 1 male. In crocodilians, the temperature of egg incubation is the environmental factor determining sex. If the temperature is low, around 30˚C, the hatchlings are all females. Higher temperature, around 34˚C, hatch all males. This study was made to consider the asymptotic stability of a positive equilibrium point in a nonlinear discrete model of the basic nesting population model, which is described in three-region depending on the temperature of egg incubation. This model is based on key life-historical data and Murray’s research. To study above, we have applied the classical linearization method and P. Cull’s method and moreover, we employ non-standard discretization methods for later our Equations (6)-(8) and (15).

ASYMPTOTICAL STABILITY OF NEUTRAL REACTION-DIFFUSION EQUATIONS WITH PCAS AND THEIR FINITE ELEMENT METHODS

This paper focuses on the analytical and numerical asymptotical stability of neutral reaction-diffusion equations with piecewise continuous arguments.First,for the analytical solutions of the equations,we derive their expressions and asymptotical stability criteria.Second,for the semi-discrete and one-parameter fully-discrete finite element methods solving the above equations,we work out the sufficient conditions for assuring that the finite element solutions are asymptotically stable.Finally,with a typical example with numerical experiments,we illustrate the applicability of the obtained theoretical results.

Rectal Cancer Stages T2 and T3 Identification Based on Asymptotic Hybrid Feature Maps

Many existing intelligent recognition technologies require huge datasets for model learning.However,it is not easy to collect rectal cancer images,so the performance is usually low with limited training samples.In addition,traditional rectal cancer staging is time-consuming,error-prone,and susceptible to physicians’subjective awareness as well as professional expertise.To settle these deficiencies,we propose a novel deep-learning model to classify the rectal cancer stages of T2 and T3.First,a novel deep learning model(RectalNet)is constructed based on residual learning,which combines the squeeze-excitation with the asymptotic output layer and new cross-convolution layer links in the residual block group.Furthermore,a two-stage data augmentation is designed to increase the number of images and reduce deep learning’s dependence on the volume of data.The experiment results demonstrate that the proposed method is superior to many existing ones,with an overall accuracy of 0.8583.Oppositely,other traditional techniques,such as VGG16,DenseNet121,EL,and DERNet,have an average accuracy of 0.6981,0.7032,0.7500,and 0.7685,respectively.

Zeno’s Paradoxes and Lie Tzu’s Dichotomic Wisdom Explained with Alpha Beta (αβ) Asymptotic Nonlinear Math (Including One Example on Second Order Nonlinear Phenomena)

Zeno’s paradoxes are a set of philosophical problems that were first introduced by the ancient Greek philosopher Zeno of Elea. Here is the first attempt to use asymptotic approach and nonlinear concepts to address the paradoxes. Among the paradoxes, two of the most famous ones are Zeno’s Room Walk and Zeno’s Achilles. Lie Tsu’s pole halving dichotomy is also discussed in relation to these paradoxes. These paradoxes are first-order nonlinear phenomena, and we expressed them with the concepts of linear and nonlinear variables. In the new nonlinear concepts, variables are classified as either linear or nonlinear. Changes in linear variables are simple changes, while changes in nonlinear variables are nonlinear changes relative to their asymptotes. Continuous asymptotic curves are used to describe and derive the equations for expressing the relationship between two variables. For example, in Zeno’s Room Walk, the equations and curves for a person to walk from the initial wall towards the other wall are different from the equations and curves for a person to walk from the other wall towards the initial wall. One walk has a convex asymptotic curve with a nonlinear equation having two asymptotes, while the other walk has a concave asymptotic curve with a nonlinear equation having a finite starting number and a bottom asymptote. Interestingly, they have the same straight-line expression in a proportionality graph. The Appendix of this discussion includes an example of a second-order nonlinear phenomenon. .

An Analysis of Chinese Address Terms From the Perspective of Speech Act Theory

Address terms are an important resource for conveying relationships.In daily interactions,the use of address terms is unavoidable.Therefore,the choose of address terms is particularly critical to make communicate smoothly with people.Previous scholars have studied address terms from a wide range of perspectives.But there is not much research on Chinese address terms based on speech act theory,which is put forward by John Langshaw Austin.By observing communicative conversations,several findings have been emerged from the analysis.They are professional title,affectionate address terms,and common address terms.These findings express the existential significance of address terms,which are the premise for people to maximize their illocutionary act when communicating.Correct understanding and grasp of the use of address terms is conductive to unfolding the communicative dialogue more smoothly.

Research on the Translation of Chinese Twenty-Four Solar Terms: A Skopos Theory Perspective

In the current era of rapid development, excellent culture needs to be inherited and spread to the world. Therefore, it is essential to consider the translation of the 24 solar terms. China persists in the principle of the Belt and Road Initiative, adheres to the guidance of Chinese traditional excellent culture goes global, and enhances the influence of Chinese culture on the words, the culture of the words communicating and developing constantly. This paper analyzes and compares translations of different versions, explores the necessity of translation strategies for translation, then summaries the translation strategy, ultimately figures out the development space, ted texts and promote the exchange of Chinese and foreign cultures.

Profile of Full-Term Births in Maternity Wards of Public Hospitals in Douala Cameroon

Introduction: Pregnancy as much as childbirth constitutes a risky situation, potentially fraught with sometimes dramatic complications: maternal death. Objective: We conducted this study with the aim of establishing the profile of those giving birth in our context with the aim to anticipate operationally in the future on morbidity but more on maternal deaths. Methodology: We conducted, using a structured questionnaire, a prospective descriptive study in representative maternity wards in the city of Douala;the study variables were socio-economic, anthropometric, obstetrical and clinical. Statistical analyses were carried out with CS Pro 7.3 and SPSS version 25.0 software. The Student, Chi-square and Fischer tests were used to compare the means of the variables and the percentages. Results: We recruited 305 births for our study. The average age of our births was 28.7 years ± 6.1 with an average height of 161.6 cm ± 5.06;an average body mass index at the start of pregnancy of 28.0 kilograms/square meter and 31.3 kilograms/square meter at delivery;the average weight gain was 8.4 g ± 5.37;an average gestation of 2.84±1.90;an average parity of 2.2 ± 2.1 with an average birth interval of 27.7 months ± 23.7. The average gestational age was 39.2 weeks ± 1.21 with pregnancy pathology dominated by malaria;85.9% began their prenatal follow-up before the 14th week of amenorrhea. Conclusion: The profile of childbirth in urban Cameroon does not seem potentially dystocic compared to that of the same regional and racial area.

A Comparison between Late Preterm and Term Infants with Respiratory Distress Syndrome, Early-Onset Sepsis, and Neonatal Jaundice in Ecuadorian Newborns

Background: To examine the differences in prevalence of respiratory distress syndrome, early-onset sepsis and jaundice, between late preterm infants versus term infants in Ecuadorian newborns. Methods: Study design: Epidemiological, observational, and cross-sectional, with two cohorts of patients. Settings: IESS Quito Sur Hospital at Quito, Ecuador, from February to April of 2020. Participants: This study included 204 newborns, 102 preterm infants, 102 term infants. Results: There are significant differences between late preterm infants and term infants, with a p-value of 0.000 in the prevalence of early sepsis, 70.59% vs. 35.29%. In respiratory distress syndrome between late and term premature infants, significant differences were observed with a p-value of 0.000, the proportion being 55.58% vs. 24.51% respectively. The prevalence of jaundice is higher in term infants with a p value of 0.002, 72.55%, versus 51.96% in late preterm infants, and the mean value of bilirubins in mg/dL was higher in term infants 14.32 versus 12.33 in late preterm infants;this difference is statistically significant with a p value of 0.004. Admission to the NICU is more frequent in late preterm infants with a p-value of 0.000, being 42.16% for late preterm infants vs. 7.84% in term infants;the mean of the hospital days with p-value 0.005, was higher in late preterm infants 4.97 days vs. 3.55 days for term newborns. Conclusion: Due to the conditions of their immaturity, late preterm infants are 2.86 times more likely to present early sepsis than full-term newborns. It is shown that late preterm infants are 2.69 times more likely to have respiratory distress syndrome compared to term infants, therefore, late preterm infants have a longer hospital stay of 4.97 days versus 3.55 days in term infants. Jaundice and mean bilirubin levels are higher in term infants due to blood group incompatibility and insufficient breastfeeding.

Long-term assessment of collagenase treatment for Dupuytren’s contracture:A 10-year follow-up study

BACKGROUND Enzymatic fasciotomy with collagenase clostridium histolyticum(CCH)has revolutionized the treatment for Dupuytren’s contracture(DC).Despite its benefits,the long-term outcomes remain unclear.This study presented a comprehensive 10-year follow-up assessment of the enduring effects of CCH on patients with DC.AIM To compare the short-term(12 wk)and long-term(10 years)outcomes on CCH treatment in patients with DC.METHODS A cohort of 45 patients was treated with CCH at the metacarpophalangeal(MCP)joint and the proximal interphalangeal(PIP)joint and underwent systematic reevaluation.The study adhered to multicenter trial protocols,and assessments were conducted at 12 wk,7 years,and 10 years post-surgery.RESULTS Thirty-seven patients completed the 10-year follow-up.At 10 years,patients treated at the PIP joint exhibited a 100%recurrence.However,patients treated at the MCP joint only showed a 50%recurrence.Patient satisfaction varied,with a lower satisfaction reported in PIP joint cases.Recurrence exceeding 20 degrees on the total passive extension deficit was observed,indicating a challenge for sustained efficacy.Significant differences were noted between outcomes at the 7-year and 10-year intervals.CONCLUSION CCH demonstrated sustained efficacy when applied to the MCP joint.However,caution is warranted for CCH treatment at the PIP joint due to a high level of recurrence and low patient satisfaction.Re-intervention is needed within a decade of treatment.