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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.

The electromechanical planetary transmission system has the advantages of high transmission power and fast running speed, which is one of the important development directions in the future. However, during the operation of the electromechanical planetary transmission system, friction and other factors will lead to an increase in gear temperature and thermal deformation, which will affect the transmission performance of the system, and it is of great significance to study the influence of the temperature effect on the nonlinear dynamics of the electromechanical planetary system.

The effects of temperature change, motor speed, time-varying meshing stiffness, meshing damping ratio and error amplitude on the nonlinear dynamic characteristics of electromechanical planetary systems are studied by using bifurcation diagrams, time-domain diagrams, phase diagrams, Poincaré cross-sectional diagrams, spectra, etc.

The results show that when the temperature rise is less than 70 °C, the system will exhibit chaotic motion. When the motor speed is greater than 900r/min, the system enters a chaotic state. The changes in time-varying meshing stiffness, meshing damping ratio, and error amplitude will also make the system exhibit abundant bifurcation characteristics.

Based on the principle of thermal deformation, taking into account the temperature effect and nonlinear parameters, including time-varying meshing stiffness and tooth side clearance as well as comprehensive errors, a dynamic model of the electromechanical planetary gear system was established.

The purpose of this paper is to have a deeper understanding of the nonlinear relationship between the impact of climate change on tourism development. Current studies on the effects of climate change on tourism development primarily rely on linear correlation assumptions.

Based on the New Institutional Economics theory, the institutional setting inherently motivates and ensures the growth of the tourism industry. For a precise evaluation of the nonlinear consequences of climate change on tourism, this paper concentrates on Chinese cities between 2011 and 2021, methodically analyzing the influence of climate change on tourism.

The study findings suggest that there is an “inverse U”-shaped nonlinear relationship between climate change and tourism development, initially strengthening and subsequently weakening. Based on these findings, the research further delves into how institutional contexts shape the nonlinear association between climate change and tourism growth. It was found that in a higher institutional backdrop, the “inverse U” curve tends to flatten and surpass the curve adjusted for a lesser institutional context. Upon deeper mechanism analysis, it was observed that cities with more advanced marketization, improved industrial restructuring and enhanced educational growth exhibit a more evident “inverse U”-shaped nonlinear connection between climate change and tourism evolution.

First, previous studies on climate change and tourism development largely rely on questionnaire data (Hu et al., 2022). In contrast to these studies, this paper uses dynamic panel data, which to some extent overcomes the subjectivity and difficulty of causality identification in questionnaire data, making our research conclusions more accurate and reliable. Second, this study breaks through the linear relationship hypothesis of previous literature regarding climate change and tourism development. By evaluating the nonlinear relationship of climate change to tourism development from the institutional pressure perspective, it more intricately delineates their interplay mechanism, expanding and supplementing the research literature on the relationship mechanism between climate change and tourism development. Thirdly, the conclusions of this study are beneficial for policymakers to better understand and assess the scope of climate change impacts. It also aids relevant departments in clarifying the direction of institutional environment optimization to elevate the level of tourism development when faced with adverse impacts brought about by climate change.

Gamification design is considered an effective way of changing users' health behavior and improving their health management performance. Even though numerous studies have investigated the positive effect of gamification competition on users, little research has considered gamification's ineffectiveness and negative effects. In particular, how gamification competition affects users' technological exhaustion remains unclear.

According to flow theory and related research on gamification, this study discusses the nonlinear relationship between gamification competition and users' technological exhaustion. Furthermore, the authors analyze the moderating effect of user type (socializers and achievers) and users' health condition on this nonlinear relationship. Based on flow theory, the authors propose a series of research hypotheses. To test all research hypotheses, the authors collected information from 407 users via a questionnaire as the data for this study.

The empirical results found a U-shaped relationship between gamification competition and technological exhaustion. Technological exhaustion gradually decreases as competition increases until reaching the lowest point; after that, technological exhaustion gradually increases as competition increases. Further, being a socializer and health condition play a moderating role in the U-shaped relationship between competition and technological exhaustion.

This study's findings not only enrich the related research in flow theory and gamification, but also contribute to the effective design of gamification in health management platforms.

Might the impact of the financial stress on exchange markets be asymmetric and exposed to regime changes? Departing from the existing literature, highlighting that the domestic and foreign financial stress in terms of money market have substantial effects on exchange market, this paper aims to investigate the impacts of the bond yield spreads of three emerging countries (Mexico, Russia, and South Korea) on their exchange market pressure indices using monthly observations for the period 2010:01–2019:12. Additionally, the paper analyses the impact of bond yield spread of the US on the exchange market pressure indices of the three mentioned emerging countries. The authors hypothesized whether the negative and positive changes in the bond yield spreads have varying effects on exchange market pressure indices.

To address the research question, we measure the bond yield spread of the selected countries by using the interest rate spread between 10-year and 3-month treasury bills. At the same time, the exchange market pressure index is proxied by the index introduced by Desai et al. (2017). We base the empirical analysis on nonlinear vector autoregression (VAR) models and an asymmetric quantile-based approach.

The results of the impulse response functions indicate that increases/decreases in the bond yield spreads of Mexico, Russia and South Korea raise/lower their exchange market pressure, and the effects of shocks in the bond yield spreads of the US also lead to depreciation/appreciation pressures in the local currencies of the emerging countries. The quantile connectedness analysis, which allows for the role of regimes, reveals that the weights of the domestic and foreign bond yield spread in explaining variations of exchange market pressure indices are higher when exchange market pressure indices are not in a normal regime, indicating the role of extreme development conditions in the exchange market. The quantile regression model underlines that an increase in the domestic bond yield spread leads to a rise in its exchange market pressure index during all exchange market pressure periods in Mexico, and the relevant effects are valid during periods of high exchange market pressure in Russia. Our results also show that Russia differs from Mexico and South Korea in terms of the factors influencing the demand for domestic currency, and we have demonstrated the role of domestic macroeconomic and financial conditions in surpassing the effects of US financial stress. More specifically, the impacts of the domestic and foreign financial stress vary across regimes and are asymmetric.

This study enriches the literature on factors affecting the exchange market pressure of emerging countries. The results have significant economic implications for policymakers, indicating that the exchange market pressure index may trigger a financial crisis and economic recession.

This study probes the psychological interplay between investor sentiment and the returns of cryptocurrencies Bitcoin and Ethereum. Employing the Granger causality test, the authors aim to gauge how extensively the Fear and Greed Index (FGI) can predict cryptocurrency return movements, exploring the intricate bond between investor emotions and market behavior.

The authors used the Granger causality test to achieve research objectives. Going beyond conventional linear analysis, the authors applied Smooth Quantile Regression, scrutinizing weekly data from July 2022 to June 2023 for Bitcoin and Ethereum. The study focus was to determine if the FGI, an indicator of investor sentiment, predicts shifts in cryptocurrency returns.

The study findings underscore the profound psychological sway within cryptocurrency markets. The FGI notably predicts the returns of Bitcoin and Ethereum, underscoring the lasting connection between investor emotions and market behavior. An intriguing feedback loop between the FGI and cryptocurrency returns was identified, accentuating emotions' persistent role in shaping market dynamics. While associations between sentiment and returns were observed at specific lag periods, the nonlinear Granger causality test didn't statistically support nonlinear causality. This suggests linear interactions predominantly govern variable relationships. Cointegration tests highlighted a stable, enduring link between the returns of Bitcoin, Ethereum and the FGI over the long term.

Despite valuable insights, it's crucial to acknowledge our nonlinear analysis's sensitivity to methodological choices. Specifics of time series data and the chosen time frame may have influenced outcomes. Additionally, direct exploration of macroeconomic and geopolitical factors was absent, signaling opportunities for future research.

This study enriches theoretical understanding by illuminating causal dynamics between investor sentiment and cryptocurrency returns. Its significance lies in spotlighting the pivotal role of investor sentiment in shaping cryptocurrency market behavior. It emphasizes the importance of considering this factor when navigating investment decisions in a highly volatile, dynamic market environment.

The Polish economy has undergone major challenges and changes over the past few decades. The country's trade flows, in particular, have become more firmly tied to the country’s Western neighbors as they have grown in volume. This study examines Poland's trade balances in ten Standard International Trade Classification (SITC) sectors versus the United States of America, first testing for and isolating structural breaks in each time series. These breaks are then included in a set of the cointegration models to examine their macroeconomic determinants.

Linear and nonlinear and nonlinear autoregressive distributed lag models, both with and without dummies corresponding to structural breaks, are estimated.

One key finding is that incorporating these breaks reduces the significance of the real exchange rate in the model, supporting the hypothesis that this variable already incorporates important information. It also results in weaker evidence for cointegration of all variables in certain sectors.

This study looks only at one pair of countries, without any third-country effects.

An important country pair's trade relations is examined; in addition, the real exchange rate is shown to incorporate economic information that results in structural changes in the economy. The paper extends the existing literature by conducting an analysis of Poland's trade balances with the USA, which have not been studied in such a context so far. A strong point is a broad methodology that lets compare the results the authors obtained with different kinds of models, both linear and nonlinear ones, with and without structural breaks.

This paper aims to prepare third-order nonlinear optical (NLO) organic materials with large nonlinear optimization value, high damage threshold and ultrafast response time.

A series of novel symmetric and asymmetric compounds possessing third-order NLO properties were synthesized using 1,3,5-tribromobenzene as the basis. The photophysical and electrochemical properties, as well as the click reactions, were characterized by means of UV–VIS–NIR absorption spectroscopy and cyclic voltammetry.

The donor–acceptor chromophores were inserted into compound, making the molecule to have a broader absorption in the near-infrared regions and a narrower optical and electrochemical band gap. It also formed an electron-delocalized organic system, which has larger effects on achieving a third-order NLO response. The third-order NLO phenomenon of benzene ring complexes was experimentally studied at 532 nm using Z-scan technology, and some compounds showed the expected NLO properties.

The click products exhibit more NLO phenomena by performing different click combinations to the side groups, opening new perspectives on using the system in a variety of photoelectric applications.

Corporate social responsibility (CSR) and innovation are the two main approaches firms utilize to promote sustainable development. However, as yet, scholars have reached no consensus regarding their precise impact on construction firm performance (CFP), hindering efforts to implement effective sustainable development strategies that improve CFP. In view that a simple linear relationship may not be sufficient to capture their precise pattern, this study aims to unveil the nonlinear impact of CSR and innovation on CFP, especially when construction firms take up a distinct competitive position.

This study first proposed four hypotheses to establish a new theoretical model by incorporating CSR, innovation, CFP and construction firms' competitive position (CFCP). Then the model was tested by using 292 annual observations collected from 75 construction firms in China. A multiple regression model analysis was carried out to analyze the survey data and validate the hypotheses.

The results reveal that both CSR and innovation have a U-shaped impact on the price-to-book ratio of a construction firm, a specific CFP measure. CFCP negatively moderates the U-shaped relationship between CSR and CFP, but positively moderates the U-shaped relationship between innovation and CFP.

This study goes beyond a simple linear view, instead of unveiling the nonlinear U-shaped effects of CSR and innovation on CFP that deepen the understanding of their complex relationships in the construction industry and makes construction firms aware that CSR and innovation can only improve performance if they reach a certain level. The moderating role of CFCP provides important implications for construction firms seeking to adopt appropriate competitive strategies related to social responsibility and innovation that both promote CFP and achieve sustainable development.

The purpose of this study is to solve two unique but difficult partial differential equations: the foam drainage equation and the nonlinear time-fractional fisher’s equation. Through our methods, we aim to provide accurate solutions and gain a deeper understanding of the intricate behaviors exhibited by these systems.

In this study, we use a dual technique that combines the Aboodh residual power series method and the Aboodh transform iteration method, both of which are combined with the Caputo operator.

We develop exact and efficient solutions by merging these unique methodologies. Our results, presented through illustrative figures and data, demonstrate the efficacy and versatility of the Aboodh methods in tackling such complex mathematical models.

Owing to their fractional derivatives and nonlinear behavior, these equations are crucial in modeling complex processes and confront analytical complications in various scientific and engineering contexts.