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High levels of fine particulate matter (PM2.5) is linked to poor air quality and premature deaths, so haze pollution deserves the attention of the world. As abundant inorganic components in PM2.5, ammonium nitrate (NH4NO3) formation includes two processes, the diffusion process (molecule of ammonia and nitric acid move from gas phase to liquid phase) and the ionization process (subsequent dissociation to form ions). In this study, we discuss the impact of meteorological factors, emission sources, and gaseous precursors on NH4NO3 formation based on thermodynamic theory, and identify the dominant factors during clean periods and haze periods. Results show that aerosol liquid water content has a more significant effect on ammonium nitrate formation regardless of the severity of pollution. The dust source is dominant emission source in clean periods; while a combination of coal combustion and vehicle exhaust sources is more important in haze periods. And the control of ammonia emission is more effective in reducing the formation of ammonium nitrate. The findings of this work inform the design of effective strategies to control particulate matter pollution. [ABSTRACT FROM AUTHOR]

This paper studies the stabilization to an inverted pendulum under a delayed proportional-derivative-acceleration (PDA) feedback, which can be used to understand human balance in quiet standing. The closed-loop system is described by a neutral delay differential equation (NDDE). The optimal feedback gains (OFGs) that make the exponential decaying rate maximized are determined when the characteristic equation of the closed-loop has a repeated real root with multiplicity 4. Such a property is called multiplicity-induced dominancy of time-delay systems, and has been discussed intensively by many authors for retarded delay differential equations (RDDEs). This paper shows that multiplicity-induced dominancy can be achieved in NDDEs. In addition, the OFGs are delay-dependent, and decrease sharply to small numbers correspondingly as the delay increases from zero and varies slowly with respect to moderate delays. Thus, the inverted pendulum can be well-stabilized with moderate delays and relatively small feedback gains. The result might be understandable that the elderly with obvious response delays can be well-stabilized with a delayed PDA feedback controller. [ABSTRACT FROM AUTHOR]

This paper studies the primary response of a fractional model proposed in Cui et al. (Int J Bifurcat Chaos 31:2150135, 2021) for cerebral aneurysm at the circle of Willis, which is described by a damped fractional Duffing oscillator with both quadratic and cubic nonlinearities under an external harmonic excitation. By using the multiple scale method, the amplitude–frequency equation of primary resonance is obtained. When the parameter values are fixed, typical hardening or softening characteristics of the oscillator are observed as the excitation frequency changes. The newly introduced number κ , a combination of the nonlinear stiffness coefficients and the natural frequency, plays an important role in creating typical hardening or softening characteristics. When the excitation frequency is fixed, characteristics similar to hardening or softening spring as well as other kinds of characteristics are also observed as a parameter changes. The flexibility of using the amplitude–frequency equation to estimate the amplitude of the resonant solutions is verified numerically when the excitation frequency is close to the natural frequency of the oscillator, and the implication of the obtained results is suggested. [ABSTRACT FROM AUTHOR]

Multi-delayed systems, especially the neutral ones, have infinitely many and complex distributed characteristic roots that are crucial for system dynamics. The definite integral method, which determines the system stability by using only a definite integral, is extended in this paper for calculating all the characteristic roots in an arbitrarily given area on the complex plane of both retarded and neutral multi-delayed systems with constant discrete delays. Two simple algorithms are proposed for implementing the proposed method, by first calculating the distribution of the real parts of all the characteristic roots, then the imaginary parts by using an iteration method. The real part distribution can be used for the quick estimation of key characteristic roots such as the rightmost ones or the corresponding accumulation point(s), thus allowing adjusting the upper limit of the integral to further simplify the calculation procedure. Examples are given to show the feasibility and the efficiency of the proposed method through numerical analyses. [ABSTRACT FROM AUTHOR]

Rolling resistance and angle constraint are important factors affecting the control performance and dynamics of Two-Wheeled Inverted Pendulums (TWIPs, for short), but they are usually neglected in previous studies. Taking both factors into account, this paper presents new control designs for the angle control of the pendulum, for the velocity control and the position control of the TWIP system. Firstly, based on dimensionality reduction and the nonlinear dynamics of the inverted pendulum, a controller with simple structure is designed for controlling the pendulum angle when the rolling resistance is precisely known. Then an improved robust controller against the unknown rolling resistance is designed for the pendulum angle. Secondly, by using the dynamics theory of slow-fast systems, velocity and position controllers for the wheels of the TWIP system are proposed with known and unknown rolling resistance. In the position control, the overshoots can be adjusted close enough to zero. Numerical examples are given to verify and demonstrate the theoretical results. [ABSTRACT FROM AUTHOR]

Stability analysis has been always a key issue in nonlinear dynamics and engineering applications, and it is still a challenging task for time-delay control systems when tuning some parameters like feedback gains and delays. In this paper, firstly we propose a parametric continuation algorithm for calculating the rightmost characteristic root(s), by solving initial value problems of a nonlinear differential equation associated with the characteristic function of the time-delay system. Then we study the static bifurcation caused by multiple characteristic roots that occurs in solving the associated nonlinear initial value problems and present an algorithm for fast calculation of the bifurcation points. We demonstrate the theoretical results with examples arising in vibration control. [ABSTRACT FROM AUTHOR]

This paper presents a control design method for implementing planar turning motion of a two-wheeled inverted pendulum with an input delay. The control task requires that the inverted pendulum is kept stabilized during the whole turning motion process along a pre-settled curve. Firstly, by using the theory of planar curve, key observations about the motion law of the two-wheeled mobile chassis are made and they are used to set up a dynamical trajectory tracking target. Then, by adjusting the parameters in the tracking target and the weights in the quadratic performance criterion, the optimal integral sliding mode controller based on a linear quadratic regulator is designed for keeping the vehicle body stabilized and tracking a circular path for the two-wheeled inverted pendulum. An illustrative example is given to demonstrate the validity of the theory with numerical simulation. [ABSTRACT FROM AUTHOR]

Despite the intensive studies on neurons, the control mechanism in real interactions of neurons is still unclear. This paper presents an understanding of this kind of control mechanism, controlling a neuron by stimulating another coupled neuron, with the uncertainties taken into consideration for both neurons. Two observers and a differentiator, which comprise the first-order low-pass filters, are first designed for estimating the uncertainties. Then, with the estimated values combined, a robust nonlinear controller with a saturation function is presented to track the desired membrane potential. Finally, two typical bursters of neurons with the desired membrane potentials are proposed in the simulation, and the numerical results show that they are tracked very well by the proposed controller. [ABSTRACT FROM AUTHOR]

We analyze the influences of the initial ramps of relaxation and creep tests on the determination of the parameters of the Scott-Blair's model, the simplest model with a fractional derivative. The true input of a test is a constant with an initial ramp. The error resulted from neglecting the initial ramp increases with the increasing of the fractional order, and the closer the data are to the beginning, the larger the errors are. Based on the error analysis, an n-times rule is generalized from the ten-times rule. For illustration, the Scott-Blair's model is fitted with the experimental data in literature. The data are of two polymer samples, PMMA and PTFE (methylmethacrylate and polytetrafluorethylene), and self-healing and thermoreversible rubbers. [ABSTRACT FROM AUTHOR]

In the dynamics analysis and synthesis of a controlled system, it is important to know for what feedback gains can the controlled system decay to the demanded steady state as fast as possible. This article presents a systematic method for finding the optimal feedback gains by taking the stability of an inverted pendulum system with a delayed proportional-derivative controller as an example. First, the condition for the existence and uniqueness of the stable region in the gain plane is obtained by using the D-subdivision method and the method of stability switch. Then the same procedure is used repeatedly to shrink the stable region by decreasing the real part of the rightmost characteristic root. Finally, the optimal feedback gains within the stable region that minimizes the real part of the rightmost root are expressed by an explicit formula. With the optimal feedback gains, the controlled inverted pendulum decays to its trivial equilibrium at the fastest speed when the initial values around the origin are fixed. The main results are checked by numerical simulation. [ABSTRACT FROM AUTHOR]

This paper presents a robust integral sliding mode controller for the back-and-forth motion of a two-wheeled inverted pendulum. The control design of this nonlinear system is based on the linearized system with bounded uncertainty and with an input delay taken into account, where the uncertainty is the integrated effect of the linearization error and bounded system uncertainties. Firstly, a trajectory tacking target is selected according to the control task. Secondly, a quadratic performance criterion with large weight of tilt angle error for optimal control is introduced to 'force' the tilt angle of inverted pendulum small enough and in turn to make the linearization error small. Thirdly, a new integral state transformation is used to convert the delayed error system with uncertainty into a delay-free one, and a key relationship between the original state variable and the new state variable is founded. Finally, the robust optimal integral sliding mode controller represented in the form of predictor state is designed by choosing the optimal state of the nominal error system as the integral sliding mode manifold. Numerical simulation shows that the designed controller not only works well in implementing the control task, but also has strong robustness against system uncertainties. [ABSTRACT FROM AUTHOR]

This paper studies the nonlinear dynamics of coupled ring networks each with an arbitrary number of neurons. Different types of time delays are introduced into the internal connections and couplings. Local and global asymptotical stability of the coupled system is discussed, and sufficient conditions for the existence of different bifurcated oscillations are given. Numerical simulations are performed to validate the theoretical results, and interesting neuronal activities are observed, such as rest state, synchronous oscillations, asynchronous oscillations, and multiple switches of the rest states and different oscillations. It is shown that the number of neurons in the sub-networks plays an important role in the network characteristics. [ABSTRACT FROM AUTHOR]

Fractional differential equations are more and more used in modeling memory (history-dependent, non-local, or hereditary) phenomena. Conventional initial values of fractional differential equations are defined at a point, while recent works define initial conditions over histories. We prove that the conventional initialization of fractional differential equations with a Riemann-Liouville derivative is wrong with a simple counter-example. The initial values were assumed to be arbitrarily given for a typical fractional differential equation, but we find one of these values can only be zero. We show that fractional differential equations are of infinite dimensions, and the initial conditions, initial histories, are defined as functions over intervals. We obtain the equivalent integral equation for Caputo case. With a simple fractional model of materials, we illustrate that the recovery behavior is correct with the initial creep history, but is wrong with initial values at the starting point of the recovery. We demonstrate the application of initial history by solving a forced fractional Lorenz system numerically. [ABSTRACT FROM AUTHOR]

This paper investigates the control of Back-and-Forth motion to fetch object and Lower-Raise-Head motion to avoid obstacle of the wheeled inverted pendulum system with an input delay. In controlling the Back-and-Forth motion, the linear optimal control theory is used because the tilt angle of the pendulum is forced to be small enough by minimizing a quadratic performance criterion with large weight of tilt angle error, and the controller is represented by using predictor-based feedback. In controlling the Lower-Raise-Head motion, linearized models do not work due to the strong nonlinearity caused by big tilt angle for avoiding obstacle. Without considering yaw movement, the wheeled inverted pendulum system is decoupled, the subsystem governing the state of the tilt angle is transformed into a simple linear system by using feedback linearization. With a properly chosen trajectory tracking target, the control of Lower-Raise-Head motion is solved on the basis of optimal trajectory tracking control for linear subsystems with an input delay. Numerical simulations illustrate the effectiveness of the proposed approaches. [ABSTRACT FROM AUTHOR]

This paper reveals the dynamical behaviors of a coupled network consisting of four neural sub-networks and multiple two-way couplings of neurons between the individual sub-networks. Different types of time delays are introduced into the internal connections within the individual sub-networks and the couplings between the sub-networks. Stability switches of the network equilibrium and Hopf bifurcation are analyzed by discussing the associated characteristic equation. The conditions for the existence of different patterns of oscillations are discussed. By using the Lyapunov's second method, the global stability of the network equilibrium is studied. Numerical simulations are performed to validate the theoretical results, and rich dynamical behaviors are observed, such as synchronous oscillations, multiple stability switches between the rest state and oscillations, phase-locked oscillations, asynchronous oscillations, and the coexistence of different patterns of bifurcated oscillations. [ABSTRACT FROM AUTHOR]

The design problem of optimal feedback control for linear systems with input delays is very important in many engineering applications. Usually, the linear systems with input delays are firstly converted into linear systems without delays, and then all the design procedures are based on the delay-free linear systems. In this way, the feedback controllers are not designed in terms of the original states. This paper presents some new closed-form formula in terms of the original states for the delayed optimal feedback control of linear systems with input delays. We firstly reveal the essential role of the input delay in the optimal control design of the linear system with a single input delay: the input delay postpones the action of the optimal control only. Based on this fact, we calculate the delayed optimal control and find that the optimal state can be represented by a simple closed-form formula, so that the delayed optimal feedback control can be obtained in a simple way. We show that the delayed feedback gain matrix can be 'smaller' than that for the controlled system with zero input delay, which implies that the input delay can be considered as a positive factor. In addition, we give a general formula for the delayed optimal feedback control of time-variant linear systems with multiple input delays. To show the effectiveness and advantages of the main results, we present five illustrative examples with detailed numerical simulation and comparison. [ABSTRACT FROM AUTHOR]

The electrocatalytic oxidation of ethanol is studied on the non-noble catalysts Ni-Co/graphene and Ni/graphene supported on glass carbon electrode (GCE) in alkaline medium. The synthesized materials are characterized by X-ray diffraction, X-ray photoelectron spectroscopy, transmission electron microscopy, and scanning transmission electron microscopy. The elements of Ni-Co/graphene and Ni/graphene catalysts are characterized using energy-dispersive X-ray spectroscopy. The electrocatalytic properties of Ni-Co/graphene and Ni/graphene for ethanol oxidation are investigated by cyclic voltammetry, chronoamperometry, and Tafel plot. Compared with Ni/graphene catalyst, Ni-Co/graphene has the higher electroactivity and better stability for ethanol oxidation. The rate constant ( k) and charge-transfer coefficient ( α) are calculated for the electron exchange reaction of the modified GCE. The results indicate that Co addition could promote the oxidation reaction at the Ni/graphene catalyst. Our study demonstrates that the low-cost electrocatalyst Ni-Co/graphene has a great potential for real direct ethanol fuel cells' application. [ABSTRACT FROM AUTHOR]

This paper focuses on the stability testing of fractional-delay systems. It begins with a brief introduction of a recently reported algorithm, a detailed demonstration of a failure in applications of the algorithm and the key points behind the failure. Then, it presents a criterion via integration, in terms of the characteristic function of the fractional-delay system directly, for testing whether the characteristic function has roots with negative real parts only or not. As two applications of the proposed criterion, an algorithm for calculating the rightmost characteristic root and an algorithm for determining the stability switches, are proposed. The illustrative examples show that the algorithms work effectively in the stability testing of fractional-delay systems. [ABSTRACT FROM AUTHOR]

This paper presents a method for directly analyzing the stability of complex-DDEs on the basis of stability switches. Two novel criteria are developed for the stability of a class of complex-DDEs. These results not only generalize some known results in literature but also greatly reduce the complexity of analysis and computation. To validate the effectiveness of the proposed criteria, the stabilization problem of the extended time delay auto-synchronization (ETDAS) control and n time delay auto-synchronization (NTDAS) control are then further investigated, respectively. The numerical simulations are consistent with the above theoretical analysis. [ABSTRACT FROM AUTHOR]

Periodic solutions occur commonly in linear or nonlinear dynamical systems. In some cases, the stability of a periodic solution holds if the rightmost characteristic root has negative real part. Based on the Lambert W function, this paper presents a simple algorithm for locating the rightmost characteristic root of periodic solutions of some nonlinear oscillators with large time delay. As application, the proposed algorithm is used to study the primary resonance and 1/3 subharmonic resonance of the Duffing oscillator under harmonic excitation and delayed feedback, as well as the control problem of the van der Pol oscillator under harmonic excitation by using delayed feedback, with a number of case studies. The main advantage of this algorithm is that though very simple in implementation, it works effectively with high accuracy even if the delay is large. [ABSTRACT FROM AUTHOR]

Nanocomposites composed of cuprous oxide (CuO) and graphene were synthesized via reduction of copper(II) in ethylene glycol. This material possesses the specific features of both CuO and graphene. Its morphology was characterized by X-ray diffraction, transmission electron microscopy, scanning electron microscopy, and X-ray photoelectron spectroscopy. Cyclic voltammetry was used to evaluate the electrochemical response of a glass carbon electrode (GCE) modified with the nanocomposite towards dopamine (DA). Compared to the bare GCE, the CuO nanoparticles modified electrode and the graphene modified electrode, the nanocomposites modified electrode displays high electrocatalytic activity in giving an oxidation peak current that is proportional to the concentration of DA in the range from 0.1 to 10 μM,with a detection limit of 10 nM (S/ N = 3). The modified electrode shows excellent selectivity and sensitivity even in the presence of high concentration of uric acid and can be applied to determine DA in real samples with satisfactory results. [Figure not available: see fulltext.] [ABSTRACT FROM AUTHOR]

This paper presents an investigation on the phenomenon of delayed bifurcation in time-delayed slow-fast differential systems. Here the two delayed’s have different meanings. The delayed bifurcation means that the bifurcation does not happen immediately at the bifurcation point as the bifurcation parameter passes through some bifurcation point, but at some other point which is above the bifurcation point by an obvious distance. In a time-delayed system, the evolution of the system depends not only on the present state but also on past states. In this paper, the time-delayed slow-fast system is firstly simplified to a slow-fast system without time delay by means of the center manifold reduction, and then the so-called entry-exit function is defined to characterize the delayed bifurcation on the basis of Neishtadt’s theory. It shows that delayed Hopf bifurcation exists in time-delayed slow-fast systems, and the theoretical prediction on the exit-point is in good agreement with the numerical calculation, as illustrated in the two illustrative examples. [ABSTRACT FROM AUTHOR]

It begins with the study of damping representation of a linear vibration system of single degree of freedom (SDOF), from the view point of fractional calculus. By using the idea of stability switch, it shows that the linear term involving the fractional-order derivative of an order between 0 and 2 always acts as a damping force, so that the unique equilibrium is asymptotically stable. Further, based on the idea of stability switch again, the paper proposes a scheme for determining the stable gain region of a linear vibration system under a fractional-order control. It shows that unlike the classical velocity feedback which can adjust the damping force only, a fractional-order feedback can adjust not only the damping force, but also the elastic restoring force, and in addition, a fractional-order PDα control can either enlarge the stable gain region or narrow the stable gain region. For the dynamic systems described by integer-order derivatives, the asymptotical stability of an equilibrium is guaranteed if all characteristic roots stay in the open left half-plane, while for the systems with fractional-order derivatives, the asymptotical stability of an equilibrium is guaranteed if all characteristic roots stay within a sector in the complex plane. Analysis shows that the proposed method, based on the idea of stability switch, works effectively in the stability analysis of dynamical systems with fractional-order derivatives. [ABSTRACT FROM AUTHOR]

A correction to the article "Robust Motion Control of a Two-Wheeled Inverted Pendulum With an Input Delay Based on Optimal Integral Sliding Mode Manifold" that was published in a May 2016 issue is presented.