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To provide high torques needed to move a robot’s links, electric actuators are followed by a transmission system with a high transmission rate. For instance, gear ratios of 100:1 are often used in the joints of a robotic manipulator. This results into an actuator with large mechanical impedance (also known as nonback-drivable actuator). This in turn generates high contact forces when collision of the robotic mechanism occur and can cause humans’ injury. Another disadvantage of electric actuators is that they can exhibit overheating when constant torques have to be provided. Comparing to electric actuators, pneumatic actuators have promising properties for robotic applications, due to their low weight, simple mechanical design, low cost and good power-to-weight ratio. Electropneumatically actuated robots usually have better friction properties. Moreover, because of low mechanical impedance, pneumatic robots can provide moderate interaction forces which is important for robotic surgery and rehabilitation tasks. Pneumatic actuators are also well suited for exoskeleton robots. Actuation in exoskeletons should have a fast and accurate response. While electric motors come against high mechanical impedance and the risk of causing injuries, pneumatic actuators exhibit forces and torques which stay within moderate variation ranges. Besides, unlike direct current electric motors, pneumatic actuators have an improved weight-to-power ratio and avoid overheating problems.

The aim of this paper is to analyze a nonlinear optimal control method for electropneumatically actuated robots. A two-link robotic exoskeleton with electropneumatic actuators is considered as a case study. The associated nonlinear and multivariable state-space model is formulated and its differential flatness properties are proven. The dynamic model of the electropneumatic robot is linearized at each sampling instance with the use of first-order Taylor series expansion and through the computation of the associated Jacobian matrices. Within each sampling period, the time-varying linearization point is defined by the present value of the robot’s state vector and by the last sampled value of the control inputs vector. An H-infinity controller is designed for the linearized model of the robot aiming at solving the related optimal control problem under model uncertainties and external perturbations. An algebraic Riccati equation is solved at each time-step of the control method to obtain the stabilizing feedback gains of the H-infinity controller. Through Lyapunov stability analysis, it is proven that the robot’s control scheme satisfies the H-infinity tracking performance conditions which indicate the robustness properties of the control method. Moreover, global asymptotic stability is proven for the control loop. The method achieves fast convergence of the robot’s state variables to the associated reference trajectories, and despite strong nonlinearities in the robot’s dynamics, it keeps moderate the variations of the control inputs.

In this paper, a novel solution has been proposed for the nonlinear optimal control problem of robotic exoskeletons with electropneumatic actuators. As a case study, the dynamic model of a two-link lower-limb robotic exoskeleton with electropneumatic actuators has been considered. The dynamic model of this robotic system undergoes first approximate linearization at each iteration of the control algorithm around a temporary operating point. Within each sampling period, this linearization point is defined by the present value of the robot’s state vector and by the last sampled value of the control inputs vector. The linearization process relies on first-order Taylor series expansion and on the computation of the associated Jacobian matrices. The modeling error which is due to the truncation of higher-order terms from the Taylor series is considered to be a perturbation which is asymptotically compensated by the robustness of the control algorithm. To stabilize the dynamics of the electropneumatically actuated robot and to achieve precise tracking of reference setpoints, an H-infinity (optimal) feedback controller is designed. Actually, the proposed H-infinity controller for the model of the two-link electropneumatically actuated exoskeleton achieves the solution of the associated optimal control problem under model uncertainty and external disturbances. This controller implements a min-max differential game taking place between: (i) the control inputs which try to minimize a cost function which comprises a quadratic term of the state vector’s tracking error and (ii) the model uncertainty and perturbation inputs which try to maximize this cost function. To select the stabilizing feedback gains of this H-infinity controller, an algebraic Riccati equation is being repetitively solved at each time-step of the control method. The global stability properties of the H-infinity control scheme are proven through Lyapunov analysis.

Pneumatic actuators are characterized by high nonlinearities which are due to air compressibility, thermodynamics and valves behavior and thus pneumatic robots require elaborated nonlinear control schemes to ensure their fast and precise positioning. Among the control methods which have been applied to pneumatic robots, one can distinguish differential geometric approaches (Lie algebra-based control, differential flatness theory-based control, nonlinear model predictive control [NMPC], sliding-mode control, backstepping control and multiple models-based fuzzy control). Treating nonlinearities and fault tolerance issues in the control problem of robotic manipulators with electropneumatic actuators has been a nontrivial task.

The novelty of the proposed control method is outlined as follows: preceding results on the use of H-infinity control to nonlinear dynamical systems were limited to the case of affine-in-the-input systems with drift-only dynamics. These results considered that the control inputs gain matrix is not dependent on the values of the system’s state vector. Moreover, in these approaches the linearization was performed around points of the desirable trajectory, whereas in the present paper’s control method the linearization points are related with the value of the state vector at each sampling instance as well as with the last sampled value of the control inputs vector. The Riccati equation which has been proposed for computing the feedback gains of the controller is novel, so is the presented global stability proof through Lyapunov analysis. This paper’s scientific contribution is summarized as follows: (i) the presented nonlinear optimal control method has improved or equally satisfactory performance when compared against other nonlinear control schemes that one can consider for the dynamic model of robots with electropneumatic actuators (such as Lie algebra-based control, differential flatness theory-based control, nonlinear model-based predictive control, sliding-mode control and backstepping control), (ii) it achieves fast and accurate tracking of all reference setpoints, (iii) despite strong nonlinearities in the dynamic model of the robot, it keeps moderate the variations of the control inputs and (iv) unlike the aforementioned alternative control approaches, this paper’s method is the only one that achieves solution of the optimal control problem for electropneumatic robots.

The use of electropneumatic actuation in robots exhibits certain advantages. These can be the improved weight-to-power ratio, the lower mechanical impedance and the avoidance of overheating. At the same time, precise positioning and accurate execution of tasks by electropneumatic robots requires the application of elaborated nonlinear control methods. In this paper, a new nonlinear optimal control method has been developed for electropneumatically actuated robots and has been specifically applied to the dynamic model of a two-link robotic exoskeleton. The benefit from using this paper’s results in industrial and biomedical applications is apparent.

A comparison of the proposed nonlinear optimal (H-infinity) control method against other linear and nonlinear control schemes for electropneumatically actuated robots shows the following: (1) Unlike global linearization-based control approaches, such as Lie algebra-based control and differential flatness theory-based control, the optimal control approach does not rely on complicated transformations (diffeomorphisms) of the system’s state variables. Besides, the computed control inputs are applied directly on the initial nonlinear model of the electropneumatic robot and not on its linearized equivalent. The inverse transformations which are met in global linearization-based control are avoided and consequently one does not come against the related singularity problems. (2) Unlike model predictive control (MPC) and NMPC, the proposed control method is of proven global stability. It is known that MPC is a linear control approach that if applied to the nonlinear dynamics of the electropneumatic robot, the stability of the control loop will be lost. Besides, in NMPC the convergence of its iterative search for an optimum depends on initialization and parameter values selection and consequently the global stability of this control method cannot be always assured. (3) Unlike sliding-mode control and backstepping control, the proposed optimal control method does not require the state-space description of the system to be found in a specific form. About sliding-mode control, it is known that when the controlled system is not found in the input-output linearized form the definition of the sliding surface can be an intuitive procedure. About backstepping control, it is known that it cannot be directly applied to a dynamical system if the related state-space model is not found in the triangular (backstepping integral) form. (4) Unlike PID control, the proposed nonlinear optimal control method is of proven global stability, the selection of the controller’s parameters does not rely on a heuristic tuning procedure, and the stability of the control loop is assured in the case of changes of operating points. (5) Unlike multiple local models-based control, the nonlinear optimal control method uses only one linearization point and needs the solution of only one Riccati equation so as to compute the stabilizing feedback gains of the controller. Consequently, in terms of computation load the proposed control method for the electropneumatic actuator’s dynamics is much more efficient.

We provide a new characterization of the equality of two positive-definite matrices A and B, and we use this to propose several new computationally convenient statistical tests for the equality of two unknown positive-definite matrices. Our primary focus is on testing the information matrix equality (e.g. White, 1982, 1994). We characterize the asymptotic behavior of our new trace-determinant information matrix test statistics under the null and the alternative and investigate their finite-sample performance for a variety of models: linear regression, exponential duration, probit, and Tobit. The parametric bootstrap suggested by Horowitz (1994) delivers critical values that provide admirable level behavior, even in samples as small as n = 50. Our new tests often have better power than the parametric-bootstrap version of the traditional IMT; when they do not, they nevertheless perform respectably.

A transfer from a richer individual to a poorer one seems to be the most intuitive and straightforward way of reducing income inequality in a society. However, can such a transfer reduce the welfare of the society? We show that a rich-to-poor transfer can induce a response in the individuals’ behaviors which actually exacerbates, rather than reduces, income inequality as measured by the Gini index. We use this result as an input in assessing the social welfare consequence of the transfer. Measuring social welfare by Sen’s social welfare function, we show that the transfer reduces social welfare. These two results are possible even for individuals whose utility functions are relatively simple (namely, at most quadratic in all terms) and incorporate a distaste for low relative income. We first present the two results for a population of two individuals. We subsequently provide several generalizations. We show that our argument holds for a population of any size, and that the choice of utility functions which trigger this response is not singular – the results obtain for an open set of the space of admissible utility functions. In addition, we show that a rich-to-poor transfer can exacerbate inequality when we employ Lorenz-domination, and that it can decrease social welfare when we draw on any increasing, Schur-concave welfare function.

The purpose of this study is to explore the coopetition relationships between platform owners and complementors in complementary product markets. Drawing on the coopetition theory, the authors examined the evolutionary trends of the coopetition relationships between platform owners and complementors and explore the main influence factors.

The authors used Lotka–Volterra model to analyze the coopetition relationship between platform owners and complementors, including the evolutionary trends as well as the results. Considering the feasibility of sample data collection, simulation is used to verify the effects of different factors on the evolution of coopetition relationships.

The results show that there are four possible results of the competition in the complementary products market. That comprises “winner-take-all for platform owners,” “winner-take-all for complementors,” “stable competitive coexistence” and “unstable competitive coexistence,” where “stable competitive coexistence” is the optimal evolutionary state. Moreover, the results of competitive evolution are determined by innovation subjects’ interaction parameters. However, the natural growth rate, the initial market benefits of the two innovators and the overall benefits of the complementary product markets influence the time to reach a steady state.

The study provides new insights into the entry of platform owners into complementary markets, and the findings highlight the fact that in complementary product markets, platform owners and complementors should seek “competitive coexistence” rather than “winner-takes-all.” Moreover, the authors also enrich the coopetition theory by revealing the core factors that influence the evolution of coopetition relationships, which further enhance the analysis of the evolutionary process of coopetition relationships.

This chapter proposes a definition of pro-middle class growth derived from the approach of Lasso de la Vega, Urrutia, and Diez (2010) to intermediate polarization. The authors show that a sufficient condition for growth to be pro-middle class is for the growth rate of what we define as the “intermediate median income” of the whole population to be higher than that of the weighted average of the growth rates of the rich and smaller than the weighted average growth rate of the poor, the “rich” and the “poor” being respectively those with an income higher and lower than the median income. An empirical illustration based on Israeli data for the period 1995–2018 indicates that in absolute terms growth was not pro-middle class for any income type. In contrast, growth was pro-middle class in relative terms for all market incomes (individual income from salaried work, individual wage per hour worked, household economic income, total household income and total equivalized income). But growth was not pro-middle class for net income and net equivalized income, even in relative terms. These conclusions appear to be related to the combined effect of developments in labor force participation, welfare policy changes and major modifications in income tax rates. The intermediate polarization measures indicate that in general there was no pro-middle class growth except in the case of specific market income types.

The purpose of the study is to perform elastic stress and deformation analysis of a functionally graded hollow disk under different conditions (rotation, gravity, internal pressure, temperature with variable heat generation) and their combinations.

The classical method of solution, Navier's equation, is used to solve the governing equation. The analysis considers thermal and mechanical boundary conditions and takes into account the variation of material properties according to a power law function of the radius of the disk and grading parameter.

The findings of the study reveal distinct trends and behaviors based on different grading parameters. The influence of gravity is found to be negligible, resulting in similar patterns to the pure rotation case. Variable heat generation introduces non-linear temperature profiles and higher displacements, with stress values influenced by grading parameters.

The study provides valuable insights into the behavior of displacement and stresses in hollow disks, offering a deeper understanding of their mechanical response under varying conditions. These insights can be useful in the design and analysis of functionally graded hollow disks in various engineering applications.

The originality and value of this study lies in the consideration of various loading combinations of rotation, gravity, internal pressure and temperature with variable heat generation. Furthermore, the study of effect of various angular rotations, temperatures and pressures expands the understanding of the mechanical behavior of such structures, contributing to the existing body of knowledge in the field.

This paper aims to study Irreversible conversion processes, which examine the spread of a one way change of state (from state 0 to state 1) through a specified society (the spread of disease through populations, the spread of opinion through social networks, etc.) where the conversion rule is determined at the beginning of the study. These processes can be modeled into graph theoretical models where the vertex set V(G) represents the set of individuals on which the conversion is spreading.

The irreversible k-threshold conversion process on a graph G=(V,E) is an iterative process which starts by choosing a set S_0?V, and for each step t (t = 1, 2,…,), S_t is obtained from S_(t−1) by adjoining all vertices that have at least k neighbors in S_(t−1). S_0 is called the seed set of the k-threshold conversion process and is called an irreversible k-threshold conversion set (IkCS) of G if S_t = V(G) for some t = 0. The minimum cardinality of all the IkCSs of G is referred to as the irreversible k-threshold conversion number of G and is denoted by C_k (G).

In this paper the authors determine C_k (G) for generalized Jahangir graph J_(s,m) for 1 < k = m and s, m are arbitraries. The authors also determine C_k (G) for strong grids P_2? P_n when k = 4, 5. Finally, the authors determine C_2 (G) for P_n? P_n when n is arbitrary.

This work is 100% original and has important use in real life problems like Anti-Bioterrorism.

Inferences for multicomponent reliability is derived for a family of inverted exponentiated densities having common scale and different shape parameters.

Different estimates for multicomponent reliability is derived from frequentist viewpoint. Two bootstrap confidence intervals of this parametric function are also constructed.

Form a Monte-Carlo simulation study, the authors find that estimates obtained from maximum product spacing and Right-tail Anderson–Darling procedures provide better point and interval estimates of the reliability. Also the maximum likelihood estimate competes good with these estimates.

In literature several distributions are introduced and studied in lifetime analysis. Among others, exponentiated distributions have found wide applications in such studies. In this regard the authors obtain various frequentist estimates for the multicomponent reliability by considering inverted exponentiated distributions.

Nitrous oxide (N₂O) use for recreational purposes appears to have increased among young people in several countries, including Denmark, Australia, The Netherlands and the UK. This increase has prompted concern among health authorities and politicians. The purpose of this paper is to map out findings in the available literature about N₂O use among young people to better understand current trends and contextualize the public concerns and the new policy responses to it.

The authors draw here on a range of sources, including research literature, reports and policy documents in English and Danish. Given the broad aim, the authors used a scoping study approach (Arksey and O’Malley, 2005).

The authors found literature on prevalence of use, health effects and policy regulations. The literature suggests that health harms associated with N₂O use are generally associated with intensive and long-term use, and death is more likely where the means of administration entails a risk of suffocation. Overall, however, the analysis shows that substantial gaps exist in the available literature. The authors lack detailed knowledge on several issues, including comparable prevalence data of N₂O use; the extent to which N₂O is used with other drugs; how one can distinguish between harmful and non-harmful use in terms of both quantity inhaled and mode of administration; and on intended and unintended consequences of policy responses to this use.

The current increase and trend in inhaling N₂O for intoxication among young people is under researched. This general review maps out what kind of knowledge would be valuable to have for prevention, harm reduction and policy interventions.

The purpose of this paper is to present and analyze the iterative rules determining the impulsive behavior of a rigid disk having a single or possibly multiple frictionless impact with two walls forming a corner.

In the first part, two theoretical iterative rules are presented for the cases of ideal impact and Newtonian frictionless impact with global dissipation index. In the second part, a numerical version of both the theoretical algorithms is presented.

The termination analysis of the algorithms differentiates the two cases: in the ideal case, it is shown that the algorithm always terminates and the disk exits from the corner after a finite number of steps independently of the initial impact velocity of the disk and the angle formed by the walls; in the non-idealcase, although is not proved that the disk exits from the corner in a finite number of steps, it is shown that its velocity decreases to zero, so that the termination of the algorithm can be fixed through an “almost at rest” condition. It is shown that the stable version of the algorithm is more robust than the theoretical ones with respect to noisy initial data and floating point arithmetic computation. The outputs of the stable and theoretical versions of the algorithms are compared, showing that they are similar, even if not coincident, outputs. Moreover, the outputs of the stable version of the algorithm in some meaningful cases are graphically presented and discussed.

The paper clarifies the applicability of theoretical methods presented in Pasquero (2018) by analyzing the paradigmatic case of the disk in the corner.