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Sufficient conditions are given for the existence of solutions of bifunction-set optimization problems, whose underlying sets are complete metric spaces. The main result of this paper is formulated in Theorem 3.1, with the help of some new data. The advantage of introducing the new data is that, by choosing suitable new data, we can obtain existence results with assumptions, that are imposed directly on the objective maps, or that are formulated via scalarization. The main result is applied successfully to Kuroiwa set optimization problems and Ky Fan vector inequality problems. We also discuss equivalences between the existence of solutions of the bifunction-set optimization problem, an Ekeland-type variational principle and a Caristi-type fixed point theorem. Examples are provided.

Lower and upper semicontinuity results for the approximate solution mapping of the parametric bifunction-set optimization problem are established under new assumptions that are quite different from the ones used previously in the case of exact solution mapping. Applications to the stability study of the approximate solution mapping of a parametric Kuroiwa set optimization problem and a parametric vector Ky Fan inequality problem are given. To our knowledge, our stability results are original. Several examples are provided.

This paper presents the parameter estimator-integrated sliding mode control of dual arm robots. To do so, a robust adaptive controller is designed for 3D cooperative motion of dual-arm robots based on the frame of second-order sliding mode control (SOSMC). Additionally, the method of the model-reference adaptive control (MRAC) is also utilized for constituting an adaptation mechanism then integrating it into the control loop to estimate the unknown robot parameters. By doing so, the proposed controller is robust with disturbances and parametric uncertainties. Furthermore, the adaptive behavior is also achieved in which the control system does not need the information of many system parameters. Finally, the applicability and feasibility of the proposed controller is presented through a 4 four degree-of-freedoms (DOFs) dual-arm manipulator.

An adaptive robust control system is considered for dual-arm manipulators (DAM) using the combination of second-order sliding mode control (SOSMC) and neural networks. The SOSMC deals with the system robustness when faced with external disturbances and parametric uncertainties. Meanwhile, the radial basis function network (RBFN) is to constitute an adaptation mechanism for approximating the unknown dynamic model of DAM. The stability of model estimator-integrated controller is analyzed using Lyapuov theory. To show the effectiveness of proposed controller, a four DOFs-DAM is applied as an illustrating example. The results reveal that the controller works well, excellently adapt to no information of robot modeling.

This paper is concerned with some sufficient conditions ensuring the stochastic stability and the almost sure exponential stability of stochastic differential equations on time scales via Lyapunov functional methods. This work can be considered as a unification and generalization of works dealing with these areas of stochastic difference and differential equations.

Metamaterials nowadays continue to gain attention thanks to their special electromagnetic characteristics. An increasing number of studies are being conducted on the absolute electromagnetic absorber configurations of high impedance surface materials at a certain frequency band. These configurations are usually fabricated with a layer of metal structure based on a dielectric sheet. In this study, we present an optimal design of a novel electromagnetic absorber metamaterial configuration working at a 23-GHz frequency range (K band).

Background Cryptococcosis is an opportunistic infection caused by the encapsulated yeast Cryptococcus neoformans and most remarkably manifests in HIV-infected individuals, especially in the settings of very low CD4 count. Development of cryptococcosis in HIV-uninfected individuals is exceedingly rare and usually signifies a marked immunodeficiency. Cryptococcosis in association with myasthenia gravis or thymoma has been previously documented in only very few cases in the literature. Case presentation We reported a complicated case of severe cutaneous cryptococcosis in a 39-year-old Vietnamese male patient with myasthenia gravis on long-term immunosuppressive therapy. The patient presented with a five month history of recurrent and progressive skin lesions that later on progressed into cryptococcal meningitis. Conclusion Through this case, we aimed to emphasize the importance of including cutaneous cryptococcosis in the differential diagnosis of cutaneous lesions in patients on chronic immunosuppressive therapy. The cutaneous manifestations of cryptococcosis can be the first clue for a disseminated disease, which makes early recognition crucial and life-saving.

This paper proposes a second-order sliding mode controller for a three-dimensional overhead crane in an extremely complicated operation with uncertain system parameters. Three actuators composed of trolley-moving, bridge-traveling, and cargo-hoisting forces simultaneously drive fine outputs comprising bridge motion, trolley translation, cable length, and two payload swing angles. Simulation and experiment are performed to investigate the controller qualities. The proposed controller asymptotically stabilizes and consistently maintains system response even when some system parameters are extensively varied.

In this paper, we give sufficient conditions for the existence of efficient solutions of a generalized vector quasi-equilibrium problem in topological vector spaces. The motivations for introducing this problem come from practical problems in traffic networks and the optimal control theory for discrete-time dynamical systems. The main results of the paper are proven with the help of a strongly monotonic function which can be constructed from the data of the problem under consideration. Some notions of cone-semicontinuity of set-valued maps, weaker than the usual concepts of semicontinuity, are also used in our study. As applications, we obtain existence results in vector quasi-optimization problems, Stampacchia set-valued vector quasi-variational inequality problems and Pareto vector quasi-saddle point problems. All these results are different from the corresponding ones in the literature.

Based on partial feedback linearization, an improved nonlinear controller is analyzed and designed for the three-dimensional motion of an overhead crane. Three control inputs composed of bridge moving, trolley travelling, and cargo hoisting forces are used to drive five state variables consisting of bridge motion, trolley movement, cargo hoisting displacement, and two cargo swing angles. The control scheme is constituted by linearly combining two components that are separately obtained from the nonlinear feedback of actuated and un-actuated states. To verify the quality of the control process, both numerical simulation and experimental study are carried out. The proposed controller asymptotically stabilizes all system states.

An overhead crane transfers the payloads of various volumes and weights depending on the each operation case. The friction factors characterized by damped coefficients can be changed in connection with operating environment. This study develops an adaptive version of sliding mode controller for the overhead cranes without priori information of system parameters composed of cargo mass and damped aspects. The proposed controller simultaneously executes five duties consisted of tracking the trolley and bridge, hoisting the cargo, keeping the payload swings small during the transport process, and absolutely suppressing the cargo vibrations at destination of trolley and bridge. Both simulation and experiment results indicate that the adaptive robust controller asymptotically stabilizes all crane system responses.

This study focuses on the design of robust nonlinear controllers based on both conventional and hierarchical sliding mode techniques for double-pendulum overhead crane systems. In the first approach, a first-order sliding surface is provided and a proper control scheme is generated to stabilize the surface. In the second approach, two levels of sliding surfaces are proposed and the control scheme is designed based on the stability of the second-level surface. We also prove the stability of the first-level sliding surface. To verify the quality of the proposed controllers, simulation for a particular type of overhead crane systems is implemented. Simulation results show that all state trajectories asymptotically converged to desired values.

An overhead crane transports cargoes of various weights and volumes depending on the operation case. Friction factors characterized by damped coefficients are changeable in terms of the operating environment. In this study, an adaptive version of the sliding mode control of a crane system is developed in the case of no priori knowledge of the payload mass and damped elements. Using two inputs, namely, trolley driving force and cargo lifting force, the proposed adaptive robust controller simultaneously executes four duties, including tracking the trolley, hoisting the cargo, keeping the cargo swing small during transient state, and completely eliminating the payload angle at steady destination. Numerical simulations and experiments are conducted to investigate the quality of the proposed controller. The results show that the proposed controller works well and all system responses are asymptotically stabilized.

This paper gives sufficient conditions for the upper and lower semicontinuities of the solution mapping of a parametric mixed generalized Ky Fan inequality problem. We use a new scalarizing approach quite different from traditional linear scalarization approaches which, in the framework of the stability analysis of solution mappings of equilibrium problems, were useful only for weak vector equilibrium problems and only under some convexity and strict monotonicity assumptions. The main tools of our approach are provided by two generalized versions of the nonlinear scalarization function of Gerstewitz. Our stability results are new and are obtained by a unified technique. An example is given to show that our results can be applied, while some corresponding earlier results cannot.

The strength and durability properties of concrete with or without three types of rice husk ash (RHA), namely, amorphous, partial crystalline, and crystalline RHA, were investigates. The three types of RHA were added into concrete at a 20% replacement level. Consequently, the pozzolanic reactivity of amorphous RHA was higher than that of partial crystalline and crystalline RHA. Concrete added with amorphous RHA showed excellent characteristics in its mechanical and durability properties. The results showed that the higher the amount of crystalline silica in RHA, the lower the concrete resistivity value became. When compared with each other, concretes with 20% of the cement replaced with these types of RHA achieved similar ultrasonic pulse velocity values, but all were lower than that of the control concrete. The incorporation of these kinds of RHA significantly reduced chloride penetration. The results not only encourage the use of amorphous materials, they also support the application of crystalline or partial crystalline RHA as mineral and pozzolanic admixtures for cement.

This paper deals with the generalized vector quasivariational inclusion Problem (P1) (resp. Problem (P2)) of finding a point (z0,x0) of a set E×K such that (z0,x0)∈B(z0,x0)×A(z0,x0) and, for all η∈A(z0,x0), $$\begin{array}{l}F(z_0,x_0,\eta)\subset G(z_0,x_0,x_0)+C(z_0,x_0)\cr \mathrm{[resp.}F(z_0,x_0,x_0)\subset G(z_0,x_0,\eta)+C(z_0,x_0)],\end{array}$$ where A:E×K→2K, B:E×K→2E, C:E×K→2Y, F,G:E×K×K→2Y are some set-valued maps and Y is a topological vector space. The nonemptiness and compactness of the solution sets of Problems (P1) and (P2) are established under the verifiable assumption that the graph of the moving cone C is closed and that the set-valued maps F and G are C-semicontinuous in a new sense (weaker than the usual sense of semicontinuity).

In this paper, we give sufficient conditions for the upper semicontinuity property of the solution mapping of a parametric generalized vector quasiequilibrium problem with mixed relations and moving cones. The main result is proven under the assumption that moving cones have local openness/local closedness properties and set-valued maps are cone-semicontinuous in a sense weaker than the usual sense of semicontinuity. The nonemptiness and the compactness of the solution set are also investigated.

Existence theorems are given for the problem of finding a point (z 0,x 0) of a set E × K such that $$(z_0,x_0)\in B(z_0,x_0)\times A(z_0,x_0)$$ and, for all $$\eta\in A(z_0,x_0), (F(z_0,x_0,x_0,\eta), C(z_0,x_0,x_0,\eta))\in \alpha$$ where ? is a relation on 2 Y (i.e., a subset of 2 Y × 2 Y ), $$A : E\times K\longrightarrow 2^K,$$ $$B : E\times K\longrightarrow 2^E, C : E\times K\times K\times K\longrightarrow 2^Y$$ and $$F : E\times K\times K\times K\longrightarrow 2^Y$$ are some set-valued maps, and Y is a topological vector space. Detailed discussions are devoted to special cases of ? and C which correspond to several generalized vector quasi-equilibrium problems with set-valued maps. In such special cases, existence theorems are obtained with or without pseudomonotonicity assumptions.