This paper deals with a comprehensive modelling and identification approach for a pneumatically actuated serial manipulator dedicated for the collaborative handling of loads attached to the end-effector, employing pneumatic artificial muscles (PAMs) as driving elements. The overall system is decomposed into two interconnected subsystems. The pneumatic subsystem covers the characteristic behaviour of the PAMs, and the air-mass-flow characteristic of the associated valves. Two different polynomial formulations replicate both the force and volumetric changes of the muscles with high fidelity. To address the hysteresis of the PAMs, a generalized Bouc-Wen model is incorporated. For a control-oriented design, the valves characteristic air-mass-flow map and its inverse are obtained using the C-b method for the purpose of compensating its nonlinear behaviour. The mechanical subsystem captures the descriptions for the manipulator geometric configuration. The complete model has been validated at a balancer test rig and provides a reliable foundation for a subsequent nonlinear control design.

ABSTRACT This paper is concerned with the constructive, modular and easy to implement passivity-based rate-dependent modelling of piezoelectric actuators (PZAs) using the port Hamiltonian (PH) framework. The proposed model incorporates hysterons to capture the hysteresic behaviour of PZAs, resulting in a causal bond-graph representation and a simplified explicit PH formulation. The proposed model is an input-affine port-Hamiltonian system that is shown to be asymptotically stable with respect to an arbitrary equilibrium configuration. The model is experimentally validated over a large range of operation frequencies using a commercial piezoelectric actuator and compared to a Bouc-Wen model of the same order.

ABSTRACT The existence, uniqueness and stability of the solution of a class of fractional-order delayed fuzzy cellular neural networks are discussed. Different from previous literature, the effects of reaction-diffusion, impulsive perturbations and time-varying delays are under consideration. The analysis can be applied to the qualitative theory of different classes of fractional-order neural network models in engineering, biology and medicine. First, the Lyapunov function method is used. A positive definite Lyapunov function is constructed, and parameters are computed to make its derivatives are negative definite, thus obtaining the global Mittag-Leffler stability criterion. Second, the compression mapping method is used to obtain the criterion of existence and uniqueness of the solution. The state update of a neural network can be viewed as a mapping, and if this mapping is compressed, there is a unique solution. Finally, two numerical examples are given to show the effectiveness and characteristics of the obtained theoretical results.

ABSTRACT Dengue fever, an ancient yet persistent global health threat transmitted by mosquitoes, remains difficult to control. Recent advances propose genetically modified hybrid mosquitoes as a novel intervention. This study focuses on two primary control strategies: the Sterile Insect Technique (SIT) and genetic sterilization. SIT involves releasing sterile male mosquitoes to reduce populations through unsuccessful mating, while genetic sterilization targets mosquito reproduction or virus transmission capabilities. In our proposed model, modified mosquitoes are included in the susceptible vector compartment, denoted as ℧ m . Diagnosis and treatment are modeled with parameters d 1 and d 2 . Field and laboratory studies suggest these methods effectively reduce mosquito populations and dengue incidence. A mathematical model is developed to study this strategy’s impact, incorporating the basic reproduction number R 0 and equilibrium analysis. Numerical methods are used to assess system stability and compute sensitivity indices W ξ H , ultimately demonstrating the potential for effective dengue control.

ABSTRACT This paper presents an energy stable scheme for the numerical solution of the Allen–Cahn equation. The scheme combines the Crank–Nicolson/Adams–Bashforth technique with the Galerkin method, complementing a thoughtfully designed stabilization term. While the Allen–Cahn equation is inherently nonlinear, our proposed algorithm effectively addresses this nonlinearity by utilizing the implicit nature of the resulting system of equations. Additionally, the L 2 error estimate for the fully discretized scheme is carried out in a rigorous way with the optimal error bound O ( τ 2 + h r + 1 ) . This analysis demonstrates the precision and accuracy of our approach. In tandem with the theoretical framework, we conduct comprehensive numerical experiments to assess the practical validity of our method. Our findings not only validate the theoretical results but also reveal an intriguing observation: the judiciously chosen stabilization term significantly enhances the performance of the model. This finding underscores the practical effectiveness of our proposed scheme, which consistently produces precise and reliable solutions, reaffirming existing evidence.

ABSTRACT We establish new conformable fractional Hermite-Hadamard (H–H) Mercer type inequalities for harmonically convex functions using the concept of support line. We introduce two new conformable fractional auxiliary equalities in the Mercer sense and apply them to differentiable functions with harmonic convexity. We also use Power-mean, Hölder’s and improved Hölder inequality to derive new Mercer type inequalities via conformable fractional integrals. The accuracy and superiority of the offered technique are clearly depicted through impactful visual illustrations. We also use our technique to derive new estimates for hypergeometric functions and special means of real numbers that are more precise than existing ones. Some applications are provided as well. Our results generalize and extend some existing ones in the literature.

ABSTRACT The technology of soft continuum robots represents an advance in the field of robotics to benefit a wide range of industries such as healthcare, manufacturing or environmental exploration. Soft continuum robots can be driven pneumatically by bellows as the soft continuum manipulator presented in this article. A driving torque model of the bellows considering hyperelastic material properties, friction and restoring torques is derived, whose purpose is suitability for model-based control design and subsequent trajectory generation. Hence, the driving torque model must be real-time capable. This is realized by an iterative algorithm calculating the bellows’ torque transmission by assuming a two-dimensional no-slip membrane contact. Nonlinear strain behaviours and hysteresis effects of the bellows are considered by the Ogden material model. The driving torque model’s performance is validated experimentally by measuring the external torques of the bellows.

ABSTRACT The structural stability of the hepatitis C model with the proliferation of infected and uninfected hepatocytes is investigated in this paper. The model is clinically verified to accurately reflect the viral dynamics of hepatitis C. It is demonstrated that the limit transition from the hepatitis C model to the Riccati system coupled with the diffusive terms leads to the elimination of the quadratic terms. Such a novel effect leads to the introduction of the concept of the deformed order-1 solitary solutions. The generalized operator of differentiation is used to construct the deformed order-1 solitary solutions to the Riccati system coupled with the diffusive terms. Finally, it is demonstrated that the Riccati system coupled with the diffusive terms admits non-deformed order-1 solitary solutions, which proves the structural instability of the hepatitis C model with the proliferation of infected and uninfected hepatocytes.

ABSTRACT Hepatitis B and C are viruses causing liver infections and resulting in grave secondary diseases. While there are different treatments for chronic liver infections, the process of evolving chronic diseases is still not fully understood. This paper presents an economic-inspired model for the overall health of an infected organism. The health model is based on the results of a reaction diffusion model for describing the space-dependent dynamics of virus and T cells during a liver infection. The different treatments affect the parameters of the reaction diffusion model and influence therefore the well-being of the infected person during an infection. The health model is selected in a detailed process out of a class of possible models. The presented work provides a foundation for an optimal control problem for finding the best treatment strategy.

ABSTRACT Due to limited weight and stiffness, large-scale robots are susceptible to structural oscillations during operation. In this publication, a model for the vertical dynamics of an aerial rescue ladder as an application example for large scale flexible robots is derived based on the Lagrange formalism. The model consists of five flexible segments, each using an arbitrary number of flexible modes. Kinematic loops occurring due to the type of interconnection between the telescopic elements are implicitly solved by the chosen assumed modes. Linearized system matrices are extracted from the model directly and very efficiently. In the resulting modelling process, the manipulator is solely described by its position and orientation kinematics and thus an adaption to different kinds of manipulators is straightforward. A validation against real world measurement data confirms the high accuracy of the derived model.