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This paper investigates the problem of global practical tracking by adaptive event-triggered output feedback for a class of uncertain nonlinear systems with unknown time-varying control coefficients. The nonlinear systems under consideration allow more general growth restriction, e.g., unknown constant and output-polynomial function coupled to the unmeasurable states. Based on non-separation principle, an adaptive event-triggered output feedback controller is proposed by combining dynamic high-gain scaling approach with backstepping method. It is worth emphasizing that a novel updating law of the high-gain is introduced to overcome the system nonlinearities and the serious uncertainties mentioned above. The controller proposed guarantees that the states of the resulting closed-loop systems are globally bounded, while the tracking error converges to a prescribed arbitrarily small neighborhood of the origin after a finite time. Finally, a numerical example is given to illustrate the effectiveness of the proposed approach.

This paper is concerned with the non-fragile reliable control of positive Markovian jump systems with actuator saturation based on event-triggered mechanism. First, an event-triggering condition is...

This paper investigates the event-triggered control of positive switched systems with randomly occurring actuator saturation and time-delay, where the actuator saturation and time-delay obey different Bernoulli distributions. First, an event-triggering condition is constructed based on a 1-norm inequality. Under the presented event-triggering scheme, an interval estimation method is utilized to deal with the error term of the systems. Using a co-positive Lyapunov functional, the event-triggered controller and the cone attraction domain gain matrices are designed via matrix decomposition techniques. The positivity and stability of the resulting closed-loop systems are reached by guaranteeing the positivity of the lower bound of the systems and the stability of the upper bound of the systems, respectively. The proposed approach is developed for interval and polytopic uncertain systems, respectively. Finally, two examples are provided to illustrate the effectiveness of the theoretical findings.

This paper proposes an event-triggered control for positive Markov jump systems without/with input saturation. First, an event-triggering condition is established in the form of 1-norm for positive Markov jump systems. Under the event-triggering condition, the term related to error signal between the sample state and the actual state is transformed into a form of interval uncertainty. Then, the positivity and stability of the systems are discussed by using the lower and upper bounds of interval uncertain systems, respectively. An event-triggered control law for the underlying systems is proposed by decomposing controller gain matrix into non-positive and non-negative parts. For positive Markov jump systems with input saturation, a design approach to the controller gain matrices and the corresponding controller auxiliary gain is presented. All conditions are described in terms of linear programming. Furthermore, the obtained approaches are developed for the discrete-time case. Finally, the effectiveness of the proposed design is verified via three examples.

This paper addresses the asynchronous control of positive switched systems. First, a unified controller design framework for the asynchronous control of switched positive systems is presented using linear programming and matrix transformation, where the “unified” property means that most of the asynchronous control problems of positive switched systems can be solved by employing the presented controller framework. Then, the unified controller framework is extended to the asynchronous L1 controller design of switched positive systems. Comparisons show that the unified controller design removes all restrictions in existing literature. Finally, a comparison example is given to illustrate the validity of the presented approach.

This paper investigates the problem of adaptive practical tracking via output feedback for a family of uncertain nonlinear systems with time delays and nonsymmetric dead-zone in actuator. Instead of the dead-zone inverse method, an adaptive output feedback robust control scheme is developed by extending the high-gain observer. To deal with the dead-zone nonlinearity, we combine the dynamic high-gain scaling approach and one-step Backstepping method. With the help of Lyapunov-Krasovskii functional, one proves that all closed-loop signals are bounded, while the system output tracks a broad class of bounded and time-varying reference trajectories by arbitrarily small error prescribed previously. Finally, a numerical example is given to illustrate the effectiveness of our controller.

This paper is concerned with the tracking control problem for the closed single spin-1/2 quantum ensembles. Based on the Liouville-von Neumann equation, mathematical model of dynamics for single spin-1/2 quantum ensembles are formulated as a bilinear form with states evolving on Bloch sphere. An associated matrix Lie group equation describing transfers from the initial state being an identity matrix is naturally introduced. The tracking problem for the system in question is transformed to a stabilization problem such that the control techniques are able to be used. In order to deal with the tracking problem, the Lyapunov-based feedback design method is employed to obtain the control such that the dynamics of system can converge to the reference trajectory.

This paper addresses an improved approach to dynamic output-feedback control design of positive systems. By using a simple matrix transformation technique that a matrix can be described via the sum of all its column vectors, a linear programming based controller design approach for nominal positive systems is proposed. Subsequently, the proposed approach is extended to interval positive systems. The present approach contains three merits that are different from existing ones: (i) it employs the linear programming technique while existing ones adopt the linear matrix inequalities technique; (ii) it provides a more general controller without negative restriction while existing ones may require the negativity of the controller gain matrix; (iii) it is easy to be extended to other issues of positive systems while this may not always be possible for existing approaches. Finally, a numerical example is provided to verify the effectiveness of the proposed design.

The purpose of this study is to explore the optimal control problems for a class of single spin-1/2 quantum ensembles. The system in question evolves on a manifold in ℛ3 and is modelled as a bilinear control form whose states are represented as coherence vectors. An associated matrix Lie group system with state space SO(3) is introduced in order to facilitate solving the given problem. The controllability as well as the reachable set of the system is first analysed in detail. Then, the maximum principle is applied to the optimal control for system evolving on the Lie group of special orthogonal matrices of dimension 3, with cost that is quadratic in the control input. As an illustrative example, the authors apply their result to perform a reversible logic quantum operation NOT on single spin-1/2 system. Explicit expressions for the optimal control are given which are linked to the initial state of the system.

This paper focuses on a problem of network synthesis for a class of quantum stochastic systems. The systems under consideration are of triplet-type form and stem from linear quantum optics and linear quantum circuits. A new quantum network realization approach is proposed by generalizing the scattering operator from the scalar form to a unitary matrix in network components. It shows that the triplet-type quantum stochastic system can be approximated by a quantum network which consists of some one-degree-of-freedom generalized open-quantum harmonic oscillators (1DGQHOs) via series, concatenation and feedback connections.

This paper focuses on investigating the problems of matrix representations of adjoint and anti-adjoint operators as well as computations for these matrices in multi-spin 1/2 systems. By introducing a multi-index transformation mapping, adjoint and anti-adjoint operators on tensor space as well as their matrix representations are defined to describe dynamics of multi-spin 1/2 systems. Formulas for computing these matrices of the adjoint and anti-adjoint operators in multi-spin 1/2 systems are given in terms of matrix representations of the adjoint and anti-adjoint operators in single-spin 1/2 systems.

Phase diagrams for ternary system of the Gemini cationic surfactants, N,N-long chain alkyl-2-hydroxyl-N,N,N,N-tetramethyl diammonium dichloride (GnCl2) with butanol and water have been drawn based on experimental data at 25 °C. The phase diagrams show that L phase and different liquid crystalline phases are existent in the ternary system at different components. Electric conductivity of the L phase has been studied. Small-angle X-ray scattering (SAXS), 2H (deuterium) quadrupolar splitting (2H NMR) and the polarizing-light microscope were employed to confirm the characteristic texture structures and the microstructure of three different liquid crystalline phases.

Dynamic interfacial tension between aqueous solutions of 3-dodecyloxy-2-hydroxypropyl trimethyl ammonium bromide (R12HTAB) and n-hexane were measured using the spinning drop method. The effects of the R12HTAB concentration (the concentration below the CMC) and temperature on the dynamic interfacial tension have been investigated; the reason of the change of dynamic interfacial tension with time has been discussed. The effective diffusion coefficient, Da, and the adsorption barrier, ɛa, have been obtained from the experimental data using the extended Word–Tordai equation. The results show that the dynamic interfacial tension becomes smaller while ɛa becomes higher with increasing R12HTAB concentration in the bulk aqueous phase. Da decreases from 5.56 × 10−12 m−2 s−1 to 0.87 × 10−12 m−2 s−1 while ɛa increases from 5.41 kJ mol−1 to 7.74 kJ mol−1 with the increase of concentration in the bulk solution of R12HTAB from 0.5 × 10−3 mol dm−3 to 4 × 10−3 mol dm−3. Change of temperature affects the adsorption rate through altering Da and ɛa. The value of Da increases from 5.56 × 10−12 m−2 s−1 to 13.98 × 10−12 m−2 s−1 while that of ɛa decreases from 5.41 kJ mol−1 to 5.07 kJ mol−1 with temperature ascending from 303 K to 323 K. The adsorption of surfactant from the bulk phase into the interface follows a mixed diffusion–activation mechanism, which has been discussed in the light of interaction between surfactant molecules, diffusion and thermo-motion of molecules.

Foam performance of 3-dodecyloxy-2-hydroxypropyl trimethylammonium bromide (DOHTAB) has been determined in the presence of different relative amounts of polymer and sodium bromide. The experimental results show that the foaming ability of the mixed systems of DOHTAB/polymer and DOHTAB/sodium bromide is stronger than that of the surfactant solutions in the absence of polymer and sodium bromide. Both foaming efficiency and foam stability of the surfactant solutions are evidently enhanced with increasing relative amounts of polymer and sodium bromide. The foamability of the mixture of DOHTAB/NaBr is stronger than that of the mixed system of DOHTAB/PEG or DOHTAB/PVP when the percentage composition is the same, whereas the foam stability of the former is weaker than that of the latter. The foamability and foam stability of the DOHTAB/PEG system were both better than those of the mixed system of DOHTAB/PVP at the same concentration.

The imidazolium salts bis(N-pyridylimidazoliumyl)methane hexafluorophosphate ([H2L1](PF6)2) and bis(N-picolyl)benzimidazoliumyl)methane hexafluorophosphate ([H2L2](PF6)2) as the precursors of potentially tetradentate NHC ligands were synthesized in 63–98% yields. Their reactions with Ag2O afforded silver−NHC complexes [Ag3(L1)2(CH3CN)2](PF6)3 (1) and [Ag4(L2)2(CH3CN)2](PF6)4 (2), respectively. Further reactions of these silver complexes as carbene transfer reagents yielded square-planar nickel(II) complexes [NiL1](PF6)2 (3) and [NiL2](PF6)2 (4), respectively. These silver and nickel complexes have been fully characterized by 1H and 13C NMR spectroscopy and X-ray diffraction analysis. Both 3 and 4 catalyzed Suzuki-type cross-coupling of aryl chlorides and bromides containing electron-withdrawing and electron-donating substituents. Complex 3 is a more active catalyst under mild conditions.

The foam performances of 3‐dodecoxy‐2‐hydroxypropyl trimethylammonium chloride (C12TAC) have been determined in the existence of different relative amount of polymer. The experimental results show that the foaming ability of the mixture systems of the C12TAC/PEG and C12TAC/PVP is stronger than that of the surfactant solutions in the absence of polymer, and with the increase of relative amount of polymer both foaming efficiency and foam stability of the surfactant solutions are evidently enhanced. For the aqueous solution of the surfactant, effect of temperature on foaming properties has also been examined. The results show that both the foaming ability and stability of the foams of the surfactant solutions are highest (or strongest) at 30°C.

Phase behavior of ternary systems containing 3‐dodecyloxy‐2‐hydroxypropyl trimethyl ammonium bromide (R12TAB), benzyl alcohol and water have been studied at 25±0.1°C. Ternary phase diagram of the systems shows a clear, isotropic, and low‐viscous region, a L phase, two liquid crystalline phases (lamella and hexagonal liquid crystal), and a coexisted phase of the liquid crystalline and micelles. 2H nuclear magnetic resonance (2H NMR) technology and polarizing‐light microscope were employed to confirm the symmetry structure of the liquid crystals and the boundaries for the different phases. In L phase, three types of different micelle regions (reverse micelles, normal micelles, and bicontinuous structures zones) were confirmed by means of the electric conductivity and the proton nuclear magnetic resonance spectroscopy (1H NMR) measurements. The microcosmic structures of the micelle were investigated, and the solubilizing position of benzyl alcohol were located according to the chemical shift of protons.

This paper focuses on investigating the problems of matrix representations of adjoint and anti-adjoint operators as well as computations for these matrices in multi-spin 1/2 systems. By introducing a multi-index transformation mapping, adjoint and anti-adjoint operators on tensor space as well as their matrix representations are defined to describe dynamics of multi-spin 1/2 systems. Formulas for computing these matrices of the adjoint and anti-adjoint operators in multi-spin 1/2 systems are given in terms of matrix representations of the adjoint and anti-adjoint operators in single-spin 1/2 systems.